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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