Roman C. answered • 10/21/12

Masters of Education Graduate with Mathematics Expertise

Now revised since comment below so disregard that comment.

I am assuming that you mean the width and length of the painting with the mat already placed around it is 25+4x and 21+2x inches respectively.

You probably know that the area of a rectangle is length times width.

In this case it's just (25+4x)(21+2x).

We are given that this is (714+21*25) in^{2 }so we can equate the two quantities:

(25+4x)(21+2x)=21*25+714

(25+4x)(21+2x)-21*25-714=0

Expand it:

8x^{2}+134x-714=0

Use the quadratic formula or factor:

It factors as 2(x+21)(4x-17)=0

since x>0, x=17/4=4.25 inches

Roman C.

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

Revising the above:

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

10/21/12

Mary K.

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 = -2110/22/12

Roman C.

10/23/12

Roman C.

That is, x is 1.3082 inches

10/21/12