SOLUTION: The outside measurements of a rectangular frame for a picture are 30 inches by 40 inches. The area of the rectangular picture inside the frame is 936 inches. Find the width of the

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Question 604411: The outside measurements of a rectangular frame for a picture are 30 inches by 40 inches. The area of the rectangular picture inside the frame is 936 inches. Find the width of the frame that surrounds the picture.
Answer by alicealc(293) About Me  (Show Source):
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assume that the frame has width of x inches
Picture's width = 30 - 2x (x on both sides)
Picture's length = 40 - 2x (x on both sides)

(30 - 2x)*(40 - 2x) = 936
1200+-+60x+-+80x+%2B+4x%5E2+=+936
4x%5E2+-+140x+%2B+1200+=+936
4x%5E2+-+140x+%2B+1200+-+936+=+0
4x%5E2+-+140x+%2B+264+=+0
(divide all by 4)
x%5E2+-+35x+%2B+66+=+0
(x - 33)*(x - 2) = 0
x - 33 = 0 or x - 2 = 0
x = 33 or x = 2

because the width of the frame can't be 33 (the picture's width and length will be negative if x = 33), then we take x = 2

so, the width of the frame that surrounds the picture is 2 inches