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System Message

[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Scott (Customer)

[00:00:00] a room is in the shape of a triangle. the length of the base of the triangle is 8 feet longer than its altitude. if the area of the triangle is 120 square feet, find the length of the base.

Benjamin C (Tutor)

[00:00:25] hello

Scott (Customer)

[00:00:31] hi

Benjamin C (Tutor)

[00:01:00] ok, so what have you done with this problem so far?

Scott (Customer)

[00:01:23] i am not sure how to solve it

[00:01:35] all i have is 120 for the area

[00:01:41] is that enough information?

Benjamin C (Tutor)

[00:02:00] surprisingly yes

[00:02:34] yeah, i think it's always a great idea just to draw it out first

[00:03:11] ok looks good

[00:03:16] what else do we know?

[00:04:21] ok good

[00:05:45] ok that looks good

[00:06:02] do you mind if we abbreviate some of these?

[00:06:12] let's call length "l" and altitude "a"

Scott (Customer)

[00:06:08] ok

[00:06:42] ok

Benjamin C (Tutor)

[00:06:52] ok so on the triangle we could write this

[00:07:19] does that look okay to you?

Scott (Customer)

[00:07:32] i think so

Benjamin C (Tutor)

[00:08:01] just so we're clear

[00:08:11] the bottom of the triangle is the base, which we're calling "l"

[00:08:18] in the problem it said "length of the base"

[00:08:35] and the altitude is that vertical line from the base to the tip of the triangle

[00:08:41] which we're labeling "A"

[00:09:22] ok, so do you remember what the formula for area of a triangle is?

Scott (Customer)

[00:10:14] umm

Benjamin C (Tutor)

[00:10:40] it's okay if you don't know

[00:11:20] here, i'll write it out

Scott (Customer)

[00:11:49] ok

Benjamin C (Tutor)

[00:13:02] does that look familiar?

Scott (Customer)

[00:13:31] A=1/2 BxH

Benjamin C (Tutor)

[00:13:39] perfect

[00:13:50] i just rewrote it so that it uses the letters we've been using

Scott (Customer)

[00:13:59] problem is i dont know either
of these

Benjamin C (Tutor)

[00:14:09] either of what?

[00:14:17] L and A?

Scott (Customer)

[00:14:43] base(length) or
height(altitude)

Benjamin C (Tutor)

[00:14:49] right

Scott (Customer)

[00:14:48] exactly

Benjamin C (Tutor)

[00:14:56] actually, with the information in the problem, we can figure them out

Scott (Customer)

[00:14:57] all i know is area

Benjamin C (Tutor)

[00:15:13] we know the area, and an equation relating the two

[00:15:17] this is enough to figure out both of them

[00:15:28] but we really only need to figure out the base (length)

[00:15:54] so we know Area = (1/2) L * A

[00:16:02] but we also know that the Area = 120

[00:17:30] therefore, we can say

[00:18:31] how does that look?

Scott (Customer)

[00:19:39] ok i suppose

Benjamin C (Tutor)

[00:20:39] what's not quite clear yet?

[00:21:13] seems like you're not convinced about this yet

[00:21:30] let's see if we can talk it through?

Scott (Customer)

[00:21:41] maybe i need to see it worked
out

Benjamin C (Tutor)

[00:22:30] how about if i do an example?

Scott (Customer)

[00:22:34] ok

Benjamin C (Tutor)

[00:22:44] ok we'll make it similar

[00:23:39] ok, let's say we have a triangle whose area is 6

[00:24:05] and the base is one foot shorter than the altitude

[00:24:18] so with that information we can write this

[00:24:29] (using the formula for area of a triangle)

[00:25:26] since these are both equal to the area, they are equal to each other

[00:25:32] so we can write...

[00:26:18] and now, using the other bit of information (base (length) is 1 foot shorter than the altitude)

[00:27:00] I'm going to rewrite this second one, because it will help in the end

[00:28:07] ok, so the rule in algebra

[00:28:27] if you have as many equations as you do unknowns (letters/variables), then you can solve it!

[00:28:52] i've marked the two equations in bold

[00:29:11] any idea on how to solve this system of equations?

Scott (Customer)

[00:29:21] nope

Benjamin C (Tutor)

[00:29:32] ok no problem

[00:29:37] let's try substitution

[00:29:56] we see that A = L + 1

[00:30:27] so we can substitute that into the first equation

[00:32:20] I multiplied both sides by 2 to get rid of that (1/2)

[00:32:39] then multiply L * (L + 1)

Scott (Customer)

[00:33:43] why L2 +L?

Benjamin C (Tutor)

[00:33:51] good question

Scott (Customer)

[00:33:55] i thought it was L^2+1

[00:34:11] why zero?

Benjamin C (Tutor)

[00:34:22] oops, i haven't finished writing

[00:34:23] one second

[00:34:49] in this block of four lines that i wrote

[00:35:04] in the second line, we have 12 = L * (L + 1)

[00:35:33] this means that the first L is multiplied by both of the expressions in the paretheses

[00:35:45] by both the second L and by the 1

[00:36:05] I can write an extra step in here that may make sense

Scott (Customer)

[00:36:54] this is confusing

Benjamin C (Tutor)

[00:37:33] which part are you confused about

[00:37:35] ?

Scott (Customer)

[00:37:38] i wish i knew

Benjamin C (Tutor)

[00:38:43] well let's start from the top, shall we?

Scott (Customer)

[00:38:41] am i supposed to be trying to
get a zero?

Benjamin C (Tutor)

[00:38:47] well

[00:38:56] i think the idea here is to end up with a quadratic equation

[00:39:28] so to get that we have to get something like that last line there

[00:39:48] the "0 = L^2..."

[00:40:02] then you can solve the quadratic by factoring or using the quadratic formula

[00:41:17] so what i've done is taken the information in the problem and written it down as two equations

[00:41:26] those are the two equations in bold

[00:42:32] since the area of a triangle is (1/2) L (base) * A (height)

[00:42:48] and we know the area of this specific triangle (in my problem) is 6

[00:43:27] so i can write it down as the first bold equation

[00:44:48] the other bold equation i got from the second piece of information (base (L) is one foot shorter than the altitude (A))

[00:45:28] and then added 1 to both sides

Scott (Customer)

[00:46:26] this is not making sense

[00:47:58] can we start over?

Benjamin C (Tutor)

[00:48:03] sure

Scott (Customer)

[00:49:09] step by step and slow

Benjamin C (Tutor)

[00:49:15] ok

[00:49:29] all right, we have a triangle whose area is 6

[00:49:37] square feet

[00:51:57] it looks a bit different from the first one, but it still works the same

[00:52:28] so L is the length of the base

[00:52:30] and A is the altitude

[00:53:00] and we know that the base is one foot shorter than the altitude

[00:53:16] so we can write that as an equation

[00:53:53] the base (L) is 1 foot less than altitude (A)

[00:54:00] in other words, L = A - 1

[00:54:37] does this look okay to you?

Scott (Customer)

[00:54:45] nope

[00:54:58] its alot of information and i
dont understand

Benjamin C (Tutor)

[00:56:04] Can you tell me what's confusing you, so we can figure out how to work on this together?

Scott (Customer)

[00:56:16] your going fast

[00:56:24] i cant keep up with all this

Benjamin C (Tutor)

[00:57:27] hmm ok

[00:59:05] here's our triangle

Scott (Customer)

[00:59:18] the 5 equations you wrote
hurt my head

[00:59:27] its overload

Benjamin C (Tutor)

[00:59:36] ha, i'm sorry about that

Scott (Customer)

[00:59:33] i just dont get it

Benjamin C (Tutor)

[00:59:40] i don't mean to hurt your head

Scott (Customer)

[00:59:39] too much info too fast

[00:59:45] i understand none of it

Benjamin C (Tutor)

[01:00:14] oh you can still see them?

[01:00:21] i thought i erased them

Scott (Customer)

[01:00:19] it confuses me

Benjamin C (Tutor)

[01:02:36] ok i thought i erased those but apparently you can still see them

[01:03:05] ok let's start fresh

[01:03:29] does it look clean to you?

Scott (Customer)

[01:03:47] what do you mean?

Benjamin C (Tutor)

[01:03:55] the whiteboard

Scott (Customer)

[01:04:00] sure

Benjamin C (Tutor)

[01:04:20] i made a new one and wanted to make sure we were seeing the same thing

[01:05:19] ok new triangle

[01:06:10] and the information

[01:06:44] does this make sense so far?

Scott (Customer)

[01:07:08] i suppose

Benjamin C (Tutor)

[01:08:07] ok, i'm going to rewrite length and altitude as base and height

[01:08:12] since that's what they are

[01:08:25] and we usually refer to the base and height of a triangle

[01:09:04] is this okay?

Scott (Customer)

[01:09:16] ok

Benjamin C (Tutor)

[01:09:30] we know the area is 6

[01:09:41] but we also know the formula for area of a triangle is...

[01:10:24] you with me so far?

Scott (Customer)

[01:10:42] thinking

Benjamin C (Tutor)

[01:13:01] what do you think?

Scott (Customer)

[01:13:22] i dont have enough information

[01:13:36] and these equations make no
sense

Benjamin C (Tutor)

[01:13:57] which equations

[01:13:58] ?

Scott (Customer)

[01:14:18] what would you call it?

[01:14:36] formula?

Benjamin C (Tutor)

[01:14:48] the "Area of triangle" formula?

Scott (Customer)

[01:15:11] are you asking me... because i
dont know

Benjamin C (Tutor)

[01:15:28] i'm asking which equations are not quite clear to you

[01:15:38] so i know which ones we can talk through

Scott (Customer)

[01:15:45] 2nd and 3rd

[01:16:05] 1st is just a statement

[01:16:10] nothing to solve

Benjamin C (Tutor)

[01:16:29] ok, so the 2nd equation

[01:16:42] in my problem description i said that the base is one foot shorter than the height

[01:17:30] so what i did was write out that statement as an equation

Scott (Customer)

[01:18:02] but i do not know the height

Benjamin C (Tutor)

[01:18:10] that's okay

[01:18:14] we don't need to know it yet

[01:18:27] all i'm doing is writing out the statement as an equation

[01:19:04] does that make sense?

Scott (Customer)

[01:19:30] no, i dont know the base

Benjamin C (Tutor)

[01:20:11] that's also okay

[01:20:15] we're going to figure that ou

[01:20:31] all i've done is write an equation which relates the base and the height

[01:20:47] although we don't know what they are yet

Scott (Customer)

[01:20:55] fine

Benjamin C (Tutor)

[01:21:06] but we will eventually figure them out

[01:21:29] ok, i'll rewrite Base as B and Height as H

[01:21:54] does that look okay?

Scott (Customer)

[01:23:50] i suppose, but i have no clue
how we can solve that 3rd
formula

[01:24:01] we have no information for
such a problem

Benjamin C (Tutor)

[01:24:14] well, it may look that way

[01:24:20] but we'll work through it

[01:24:30] before we get to the 3rd one i want to make sure you're clear on the 2nd one

Scott (Customer)

[01:24:53] you said you were just writing
out a formula..right?

Benjamin C (Tutor)

[01:25:20] yeah, for the 2nd equation, i rewrote the problem statement as an equation

Scott (Customer)

[01:25:28] ok

Benjamin C (Tutor)

[01:25:31] "base is one foot shorter than height"

[01:25:56] all right, now the 3rd one

[01:26:07] this is a general formula for the area of a triangle

[01:26:17] this is just something you need to know

Scott (Customer)

[01:26:38] ok

Benjamin C (Tutor)

[01:26:46] it's not given in the problem, but it's understood that you already know it or can find it in a book

Scott (Customer)

[01:26:57] if only i had the base and
height

[01:27:01]

Benjamin C (Tutor)

[01:27:12] don't fret

[01:27:26] you may not believe me but i have faith that we can find both the base and height

Scott (Customer)

[01:27:37] from the area?

Benjamin C (Tutor)

[01:27:43] yes

Scott (Customer)

[01:27:46] because thats all i got to work
with

Benjamin C (Tutor)

[01:27:51] well

[01:27:59] we kind of have three pieces of information here

[01:28:09] the three lines written down

[01:28:22] the area of this specific triangle (6)

[01:28:35] the relationship between base and height (B = H - 1)

[01:28:43] and the formula for area of any triangle

[01:29:15] we can combine these three and come up with the awesome power to find out both the base and the height!

[01:29:49] how does that sound?

Scott (Customer)

[01:30:19] i would like to see that

Benjamin C (Tutor)

[01:30:32] ok, we'll get there

[01:30:37] so, next step

[01:31:05] we know the general formula for area of a triangle

[01:31:13] and we know the area of this specific triangle

[01:31:26] so we can combine those

Scott (Customer)

[01:32:36] 6=1/2 b*h

Benjamin C (Tutor)

[01:32:52] ah, very nice!

[01:33:15] all right

[01:33:22] now the other piece of information

[01:33:24] B = H - 1

[01:33:53] for the sake of the problem, let's add a 1 to both sides

[01:34:01] so we'll get B + 1 = H

[01:34:33] sound good?

Scott (Customer)

[01:34:31] what?

[01:34:36] you lost me

Benjamin C (Tutor)

[01:34:58] we started with B = H - 1

[01:35:10] from the "base is one foot shorter than height"

Scott (Customer)

[01:35:27] so then why would we add 1

[01:35:34] we would subtract 1..right?

[01:35:38] h-1

[01:35:42] not h+1

Benjamin C (Tutor)

[01:35:56] tell you what

Scott (Customer)

[01:35:56] but we dont know what h is

Benjamin C (Tutor)

[01:36:00] let's not change it at all

[01:36:06] we'll just leave it as is

[01:37:01] ok so i'll rewrite these two lines down here

[01:37:30] does that look good?

Scott (Customer)

[01:37:38] why?

Benjamin C (Tutor)

[01:37:55] because i'm going to draw over them

[01:38:10] and i didn't want to draw more up there

[01:38:36] more arrows and circles

[01:38:58] ready for the next step?

Scott (Customer)

[01:40:10] ok

Benjamin C (Tutor)

[01:40:35] we can use the first equation

[01:40:52] and plug in that information into the second one

[01:40:59] since we know B = H - 1

[01:41:06] we can substitute B in the second one

Scott (Customer)

[01:41:12] we have no info to plug in

Benjamin C (Tutor)

[01:41:40] well, B = H - 1

[01:41:53] so instead of writing the second equation with "B"

[01:42:00] we'll rewrite it with "H - 1"

[01:42:05] because B = H - 1

[01:43:11] how does that look to you?

Scott (Customer)

[01:43:27] ok

Benjamin C (Tutor)

[01:43:59] i'd like to get rid of that (1/2)

[01:44:08] can you think of a good way to do that?

Scott (Customer)

[01:44:34] 12=h-1*h

Benjamin C (Tutor)

[01:44:56] that's pretty close

[01:45:01] don't forget the parentheses

[01:45:27] otherwise it looks good

[01:45:44] ok, now can you expand the right hand side of that equation?

Scott (Customer)

[01:46:15] hmm

[01:46:26] nope cant do it

[01:46:33] not enough info

Benjamin C (Tutor)

[01:46:50] well, i mean

[01:46:59] how can you rewrite (H - 1) * H

[01:46:59] ?

[01:47:06] you don't need to know what H is yet

Scott (Customer)

[01:47:13] i dont know

Benjamin C (Tutor)

[01:47:24] so to expand

[01:47:32] we take the H on the right

[01:47:41] and multiply it by everything inside the parentheses

Scott (Customer)

[01:48:52] Slow down. I'm confused.

Benjamin C (Tutor)

[01:49:34] ok, let's look at a small example

[01:50:36] what is (2 + 3) * 5 equal to?

Scott (Customer)

[01:50:58] 25

Benjamin C (Tutor)

[01:51:06] yep

[01:51:19] but let's expand it

[01:51:35] it may look a bit ugly but hopefully it'll help the "H" thing make more sense

[01:51:59] so to expand the stuff in the parentheses

[01:52:17] we multiply each part on the inside (2 and 3) by whatever is on the outside (5)

[01:52:21] and add them

[01:53:06] make sense?

Scott (Customer)

[01:53:40] i think so

Benjamin C (Tutor)

[01:53:59] we apply the same idea to that "H" stuff

[01:54:28] we multiply everything inside (H - 1) by that H on the outside

[01:54:45] and then subtract it, since there's a minus sign inside

[01:55:50] do you understand?

Scott (Customer)

[01:55:56] i think

[01:56:31] 12=H

Benjamin C (Tutor)

[01:57:24] oh, are you thinking that H^2 - H = H?

Scott (Customer)

[01:57:39] yes

Benjamin C (Tutor)

[01:57:50] unfortunately we can't quite do that

[01:57:51] sorry

[01:58:52] but we'll go on from what we have

[01:59:11] from the looks of this last line, we're going to have a quadratic

[01:59:22] so we'll need to bring that 12 over to the right-hand side

Scott (Customer)

[01:59:26] hows that?

Benjamin C (Tutor)

[02:00:11] since there is that H^2 expression, it will be a quadratic

[02:00:45] and in order to solve the quadratic, we'll need to have everything one one side, and zero on the other side

[02:01:33] can you do that with this equation?

Scott (Customer)

[02:01:57] what do you mean?

Benjamin C (Tutor)

[02:02:18] we need to bring the 12 to the right side of the equation

[02:02:24] how would we do that?

Scott (Customer)

[02:02:32] subtract i guess

[02:02:37] -12

Benjamin C (Tutor)

[02:02:42] sounds good to me

[02:02:52] ok, so can you rewrite the equation?

Scott (Customer)

[02:03:07] -12=h^2-h

[02:03:13] hmm

[02:03:27] 0=-12+h^2-h

Benjamin C (Tutor)

[02:03:42] excellent

[02:04:03] if you don't mind, i'll slide the -12 to the right

[02:04:34] does this look okay to you?

Scott (Customer)

[02:05:19] i suppose

Benjamin C (Tutor)

[02:05:44] do you prefer the way you wrote it?

Scott (Customer)

[02:05:57] does it matter?

Benjamin C (Tutor)

[02:06:07] not really

[02:06:29] ok anyway, we have a quadratic here

[02:06:42] can you think of any way to solve it?

Scott (Customer)

[02:06:58] no

[02:07:12] they have nothing in common

Benjamin C (Tutor)

[02:07:24] what has nothing in common?

Scott (Customer)

[02:07:37] 12 h and h

Benjamin C (Tutor)

[02:07:49] here's the thing

[02:07:59] we have an equation involving H^2 and H

[02:08:08] so there are methods that we can use to solve for H

Scott (Customer)

[02:08:33] what do you mean?

Benjamin C (Tutor)

[02:08:50] either factoring, or the quadratic formula

Scott (Customer)

[02:10:07] i dont know how that would
work

Benjamin C (Tutor)

[02:10:21] have you learned about factoring or the quadratic formula?

Scott (Customer)

[02:10:48] a bit, sure

Benjamin C (Tutor)

[02:11:22] you'll need to try that here

[02:11:30] think you can give it a shot?

Scott (Customer)

[02:11:41] i have no idea what to do

Benjamin C (Tutor)

[02:12:04] can you remember the quadratic formula?

Scott (Customer)

[02:12:20] nope

Benjamin C (Tutor)

[02:12:39] have you learned about factoring?

Scott (Customer)

[02:12:49] a little

Benjamin C (Tutor)

[02:13:11] ok, i'll do a quick factoring example

[02:15:41] since there are all pluses in this equation we know that both sets of parentheses will have pluses on the inside

Scott (Customer)

[02:16:05] 3, ?

[02:16:21] im confused

[02:16:53] forget the 3 i just dont know
what i am doing

[02:17:13] 2, 1

Benjamin C (Tutor)

[02:17:21] perfect

[02:17:44] i thought you didn't know what you're doing?

[02:18:17] anyway

Scott (Customer)

[02:18:36] but i dont have numbers

[02:18:47] i have H...?

Benjamin C (Tutor)

[02:19:04] can you do the same factoring to the equation with H?

Scott (Customer)

[02:20:06] i dont think so

Benjamin C (Tutor)

[02:20:23] it's the same idea as for the "x" equation

[02:21:01] we just don't quite know yet whether there are minuses or pluses inside the parentheses

[02:21:20] and what numbers should go in for the question marks

Scott (Customer)

[02:21:44] H and 12 have nothing in
common

[02:21:51] so i am at a loss here

Benjamin C (Tutor)

[02:22:06] ok, what did you do to solve the x equation?

Scott (Customer)

[02:22:47] i looked for what two numbers
when added make 3

[02:22:56] and multiplied make 2

Benjamin C (Tutor)

[02:23:04] exactly

Scott (Customer)

[02:23:20] 2x1=2

[02:23:26] 2+1=3

Benjamin C (Tutor)

[02:23:35] perfect

[02:23:46] so we need to apply the same idea to the H equation

[02:23:54] it's a bit more complicated but definitely possibly

[02:23:56] *possible

Scott (Customer)

[02:24:04] i dont see how thats even
possible

Benjamin C (Tutor)

[02:24:13] let's take a look

[02:24:22] we want to find what two numbers get -12 when multiplied

[02:24:31] can you think of two numbers whose product is -12?

Scott (Customer)

[02:24:45] product?

[02:24:54] is that + or x?

Benjamin C (Tutor)

[02:25:06] multiplication

Scott (Customer)

[02:25:14] 3x4=12

Benjamin C (Tutor)

[02:25:24] ok, but what about -12?

Scott (Customer)

[02:25:39] -3x4

Benjamin C (Tutor)

[02:25:46] ok let's try that

Scott (Customer)

[02:25:48] -4x3

Benjamin C (Tutor)

[02:26:04] yeah, that's another one

[02:26:25] what is -3 + 4?

Scott (Customer)

[02:26:41] 1

Benjamin C (Tutor)

[02:26:48] yep

[02:26:54] but it looks like we're trying to get -1

[02:27:00] since we have -H

[02:27:07] so -3 and 4 don't work

[02:27:13] but what about 3 and -4...

Scott (Customer)

[02:27:44] -1

Benjamin C (Tutor)

[02:27:53] yep

[02:28:05] so...

[02:28:51] we've been looking for two numbers, which when multiplied get -12

[02:28:54] and when added get -1

[02:28:58] it looks like we found them

[02:29:15] does this make sense?

Scott (Customer)

[02:29:32] why -1

Benjamin C (Tutor)

[02:29:42] because of -H

Scott (Customer)

[02:29:50] h is 1

Benjamin C (Tutor)

[02:30:04] it's "minus H"

Scott (Customer)

[02:30:13] -h is -1

Benjamin C (Tutor)

[02:30:37] look back at the example

[02:30:54] there was a +3 in front of the x

Scott (Customer)

[02:30:55] where?

Benjamin C (Tutor)

[02:31:28] +3 in front of the x, so you found two numbers who added up to +3

[02:31:56] this time we have a - in front of the H (in other words "-1") so we want to find two numbers who add up to -1

Scott (Customer)

[02:32:53] is this done?

Benjamin C (Tutor)

[02:33:01] almost...

[02:33:21] we've done the factoring, no we look at what possible values of H make this equation work

Scott (Customer)

[02:33:40] h=+3, -4

Benjamin C (Tutor)

[02:33:57] let's say H = +3

[02:34:02] plugging that in...

[02:34:42] hmm

[02:34:49] doesn't seem like that works

[02:34:59] does my math make sense here?

Scott (Customer)

[02:35:17] h=-3, +4

Benjamin C (Tutor)

[02:35:48] ok, so if you plug either of those in

[02:35:55] one of the two sets will become 0

[02:35:57] perfect

[02:36:03] so H = -3 or +4

[02:36:08] so which one is it?

[02:36:12] can H be both?

Scott (Customer)

[02:36:21] i have no idea

Benjamin C (Tutor)

[02:36:32] think about what we're looking for

[02:36:38] we're trying to find the height of a triangle

[02:37:09] could the height be -3?

Scott (Customer)

[02:37:27] no

[02:37:36] +1

Benjamin C (Tutor)

[02:37:58] +1?

Scott (Customer)

[02:38:07] H=1

[02:38:23] -3+4=1

Benjamin C (Tutor)

[02:38:40] i see

[02:38:45] actually we don't need to do that

Scott (Customer)

[02:38:45] is that the answer

Benjamin C (Tutor)

[02:39:01] H is either -3 or +4

[02:39:08] we don't need to add them

[02:39:22] as you said, H can't be -3 because you can't really have a negative height

Scott (Customer)

[02:39:22] well i dont know

Benjamin C (Tutor)

[02:39:31] so by elimination

[02:40:28] H must be 4

[02:40:59] one more final step before we have our answer

[02:41:08] in the problem we're actually looking for B, not H

[02:41:18] can you find a way to get B if we know H?

Scott (Customer)

[02:41:54] 4-1=3

[02:42:03] b=3

Benjamin C (Tutor)

[02:42:11] bingo

[02:43:18] so the problem you have, where the area is 120

[02:43:27] use the same ideas we used here

Scott (Customer)

[02:43:33] uh oh

[02:44:11]

Benjamin C (Tutor)

[02:44:56] unfortunately my time here is up

[02:45:15] so try to look over the work from this example, which is very similar to your problem

Scott (Customer)

[02:45:28] ok, thank you

Benjamin C (Tutor)

[02:45:45] you're welcome

[02:45:48] good luck, Scott