Question 38575: The mat around a picture measures x inches across. The length of the picture with the mat is 40 inches, and the width of the picture with its mat is 24 inches. If the area of the picture is 192 square inches, find the dimensions of the picture.
Thanks for answering!:-)
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! Since the border all along the picture is x, the length of just the picture is
40 - 2x (since x on top and bottom).
The width is then 24 - 2x, by the same logic.
And of course, A = LW = 192.
So, by substituting, we get
192 = (40 - 2x)(24 - 2x)
192 = 960 - 128x + 4x^2 or
4x^2 - 128x + 768 = 0
x^2 - 32x + 192 = 0
(x - 24)(x - 8) = 0
x = 24 or x = 8
but the border cannot be 24, that's too big.
So the border is 8 inches, and the dimensions of just the picture are
40 - 16 = 24 inches
by
24 - 16 = 8 inches
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