SOLUTION: The length of a picture is 4/3 times its width. It is placed in a picture frame of uniform width of 2cms. If the area is 100 sq. cms, what are the dimensions of the picture?

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Question 1005090: The length of a picture is 4/3 times its width. It is placed in a picture frame of uniform width of 2cms. If the area is 100 sq. cms, what are the dimensions of the picture?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The length of a picture is 4/3 times its width.
It is placed in a picture frame of uniform width of 2cms.
If the area is 100 sq. cms, what are the dimensions of the picture?:
:
let L = the length of the picture
let w = the width of the picture
then because of the 2" uniform width of the frame,
(L+4) = the length including the frame
(W+4) = the width including the frame
;
Assuming they mean the whole area including the frame = 100 sq/cm
(L+4) * (W+4) = 100
Given that
L = 4%2F3W, replace L
(4%2F3W+4)(W+4) = 100
FOIL
4%2F3W^2 + 16%2F3W + 4W + 16 = 100
subtract 100 from both sides
4%2F3W^2 + 16%2F3W + 4W - 84 = 0
multiply by 3, get rid of the fraction
4W^2 + 16W + 12W - 252 = 0
4W^2 + 28W - 252 = 0
Simplify, divide by 4
W^2 + 7W - 63 = 0
using the quadratic formula, the positive solution
W = 5.175 cm is the width of the picture
then
L = 4%2F3*5.175
L = 6.9 cm is the length of the picture
:
:
See if the works out
the frame dimensions are 4" longer than the picture
9.175 * 10.9 = 100.0 sq/cm