SOLUTION: A rectangular patio is 7 ft longer than it is wide. Determine the dimensions of the patio if it measures 13 ft diagonally. Please solve involving applications of polynomials.

Question 202689: A rectangular patio is 7 ft longer than it is wide. Determine the dimensions of the patio if it measures 13 ft diagonally. Please solve involving applications of polynomials.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A rectangular patio is 7 ft longer than it is wide. Determine the dimensions of the patio if it measures 13 ft diagonally. Please solve involving applications of polynomials.
.
Let w = width of rectangle
then
w+7 = length of rectangle
.
From Pythagorean theorem we have:
w^2 + (w+7)^2 = 13^2
w^2 + (w+7)(w+7) = 13^2
w^2 + (w^2+7w+7w+49) = 169
2w^2+14w+49 = 169
2w^2+14w-120 = 0
w^2+7w-60 = 0
(w-5)(w+12) = 0
w = {5, -12}
We cam throw out the negative solution leaving:
w = 5 feet(width)
.
length:
w+7 = 5+7 = 12 feet (length)
.
Dimensions of rectangle: 5x7 feet
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