SOLUTION: The mat around a picture measures x inches across. The length of the picture with its mat is 40 inches, and the width of the picture with its mat is 24 inched. If the area of the p

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Question 37543: The mat around a picture measures x inches across. The length of the picture with its mat is 40 inches, and the width of the picture with its mat is 24 inched. If the area of the picture is 192 square inches, find the dimensions of the picture.
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
Here the setup for this is
(40 - 2x)(24 - 2x) = 192
4x^2 - 128x + 960 = 192
4x^2 - 128x + 768 = 0
x^2 - 32x + 192 = 0
(x - 8)(x - 24) = 0
x = 8 or x = 24
but x = 24 is extraneous, x = 8
Therefore the dimensions of the original picture are
(40 - 16) by (24 - 16) or
24 in x 8 in