Math 209
posted by Wanda .
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?

length  x
width  x7
hypotenuse  x+1
x^2 + (x7)^2 = (x+1)^2
x^2 + x^2  14x + 49 = x^2 + 2x + 1
x^2  16x + 48=0
(x4)(x12) = 0
x = 4 or x=12 , but x > 7 to have a positive width
so x = 12
length = 12 metres
width = 5 metres