SOLUTION: a rug is rectangular in shape and is 2 feet longer than it is wide. if its diagonal is 18 feet, find its dimensions

Question 578879: a rug is rectangular in shape and is 2 feet longer than it is wide. if its diagonal is 18 feet, find its dimensions
Answer by dfrazzetto(283) (Show Source): You can put this solution on YOUR website!
Form a right triangle:
L=w+2
let a=w, b=w+2 and c=18
a^2+b^2=c^2
w^2 + (w+2)^2 = 18^2
w^2 + w^2 +4w + 4 = 324
2w^2 + 4w + 4 = 324
2w^2 + 4w - 320 = 0

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=2576 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 11.6885775404495, -13.6885775404495. Here's your graph:

Thus it is roughly 11.69 x 13.69
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