Tabitha wants to hang a painting in a gallery. The painting and frame must have an area of 58 square feet. The painting is 7 feet wide by 8 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?
Image of a frame 7 feet wide by 8 feet long, with an of x on the bottom and right sides
x2 + 15x − 2 = 0
x2 + 15x + 58 = 0
4x2 + 30x − 2 = 0
4x2 + 30x + 58 = 0

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@jim_thompson5910

##### 1 Attachment

- jim_thompson5910

|dw:1442710030323:dw|

- jim_thompson5910

|dw:1442710064925:dw|

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## More answers

- jim_thompson5910

can you tell me what this length is?
|dw:1442710140915:dw|

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15?

- jim_thompson5910

no the 7 is the vertical dimension
I'm asking for the total horizontal dimension

- jim_thompson5910

hint:
|dw:1442710233263:dw|

- help_people

30?

- jim_thompson5910

idk how you're getting that

- jim_thompson5910

do you see the stuff I circled?

- help_people

yes

- jim_thompson5910

add them up to get ???

- help_people

2x or x^2

- jim_thompson5910

x + 8 + x = ???

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7

- jim_thompson5910

think of it like this `apple + apple = 2 apples`
so `x + x = 2x`
right?

- help_people

yeah x8x?

- jim_thompson5910

so if x+x = 2x, then x+x+8 turns into what?

- help_people

2x+8

- jim_thompson5910

good

- jim_thompson5910

|dw:1442710945434:dw|

- jim_thompson5910

so hopefully you see how that total length marked in the drawing is 2x+8 feet?

- help_people

i finally do :D

- jim_thompson5910

ok great

- jim_thompson5910

what is this marked length here?
|dw:1442711082155:dw|

- help_people

2x+7?

- jim_thompson5910

good

- jim_thompson5910

|dw:1442711337192:dw|

- jim_thompson5910

now if the length was 2x+8 and the width was 2x+7, then what is the area of the rectangle?

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4x+15?

- jim_thompson5910

you have to multiply (2x+8) with (2x+7)
FOIL it out

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could you show me ?

- jim_thompson5910

have you learned the box method? that's actually better than FOIL

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4x^2+30x+56?

- jim_thompson5910

good, you used the box method to get that? or some other method?

- help_people

box method

- jim_thompson5910

ok great

- jim_thompson5910

so the entire area of the rectangle (larger rectangle) is `4x^2+30x+56`
they tell us that "The painting and frame must have an area of 58 square feet."
so equate the two areas
4x^2+30x+56 = 58

- jim_thompson5910

now get everything to one side

- help_people

how

- jim_thompson5910

subtract 58 from both sides

- jim_thompson5910

|dw:1442712284053:dw|

- jim_thompson5910

|dw:1442712322065:dw|

- jim_thompson5910

|dw:1442712342649:dw|

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4x^2+30x-2

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@jim_thompson5910

- jim_thompson5910

correct

- jim_thompson5910

0 be left on the other side (since 58-58 = 0)
so we have this answer `4x^2 + 30x - 2 = 0`

- help_people

ok wow

- help_people

tahnks alot for everything :)

- jim_thompson5910

no problem

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