SOLUTION: A painting is twice as high as it is wide. A 3" frame has a total area of 576 square inches. What are the dimensions of the painting? I already : Drew a picture frame, labeled t

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Question 560692: A painting is twice as high as it is wide. A 3" frame has a total area of 576 square inches. What are the dimensions of the painting?
I already : Drew a picture frame, labeled the width of the frame as 3 in. , labeled the width of the PICTURE as x, and labeled the length of the picture as 2x. Please help !
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A painting is twice as high as it is wide.
A 3" frame has a total area of 576 square inches.
What are the dimensions of the painting?
:
A frame of 3" will add 6" to each of the overall dimensions, (picture & frame)
:
Overall area - picture area = frame area (576 sq/in)
(2x + 6) * (x + 6) - (2x * x) = 576
FOIL
2x^2 + 12x + 6x + 36 - 2x^2 = 576
Combine like terms
2x^2 - 2x^2 + 12x + 6x = 576 - 36
18x = 540
x = 540/18
x = 30 inches is the width of the painting
then
2(30) = 60 inches is the length
:
:
Check this
(66*36) - (60*30) =
2376 - 1800 = 576