 Karena Z.

You place a mat around a 25 inch by 21 inch painting. The width of the painting is (25 in + 4x) and the length is (21in + 2x). The area of the mat is 714 sq inches. What is x?

If possible, please include steps. Thank you so much!

## 2 Answers By Expert Tutors

By: Roman C.

tutor

That is, x is 1.3082 inches

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10/21/12 Roman C.

tutor

Nevermind the equation should be (25+4x)(21+2x)=21*25+714=1239.

Revising the above:

The quadratic will be 8x2+134x-714=0 which factors as 2(x+21)(4x-17)=0 so we get x=4/17 inches

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10/21/12 Mary K.

tutor
I wasn't finished when the answer was added. Continuing..... 2 8x + 134x - 714 = 0 2(4x^2 + 67x - 357) = 0 2(x+21)(4x-17) = 0 4x - 17 = 0 4x = 17 x = 17/4 or 4.25 There is another answer which can be obtained for this equation using the factor x + 21 = 0 so x = -21
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10/22/12 Roman C.

tutor
Yes. However, notice why I solved only the second factor. x = -21 is negative and so can't be the answer as the rug-frame can't have negative thickness. Even if you interpret a negative answer as the rug extending inward from the picture perimeter, the x=-21 solution will completely cover up the picture. Who want's to see a picture completely covered up by the rug?
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10/23/12

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