# Math 209

The width of a rectangular carpet is 7 meters shorter than the length, and the diagonal is 1 meter longer than the length. What are the carpet's dimensions?

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1. length -- x
width --- x-7
hypotenuse -- x+1

x^2 + (x-7)^2 = (x+1)^2
x^2 + x^2 - 14x + 49 = x^2 + 2x + 1
x^2 - 16x + 48=0
(x-4)(x-12) = 0
x = 4 or x=12 , but x > 7 to have a positive width
so x = 12

length = 12 metres
width = 5 metres

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