If the total area of a picture measuring 10 inches by 12 inches plus a meeting of a uniform width surrounding the picture is 224 square inches, the width of the matting is...

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To find the width of the matting, you can solve a quadratic equation using the information given. We know that the new area of 224 square inches will be found by multiplying the width and the height.  If the original dimensions are 10 in by 12 in, the new dimensions would be 10 +x and 12 + x. Use these in the formula for area of a rectangle. A = (10 + x) (12 + x) 224 = x^2 + 22x + 120 -120                  -120 104 = x^2 + 22x  -104       -104 0 = x^2 + 22x -104 0 = (x + 26) (x - 4) The only answer for x that would solve this problem would be the positive 4.   The width of the matting is 4 inches. Check your answer: (10 +4) (12 + 4) 14 x 16 224 square inches.


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