SOLUTION: The oriental rug shown is 5 feet longer than it is wide. If the diagonal of the rug is 12 feet find its dimensions to the nearest tenth of a foot.

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Question 903097: The oriental rug shown is 5 feet longer than it is wide. If the diagonal of the rug is 12 feet find its dimensions to the nearest tenth of a foot.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Using Pythagorean Theorem
(w+5)^2 + w^2 = 12^2
2w^2 + 10w - 119 = 0 (Tossing out the negative solution for unit measure)
w = 5.6 and L = 10.6 5.6%2B5
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B10x%2B-119+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2810%29%5E2-4%2A2%2A-119=1052.

Discriminant d=1052 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-10%2B-sqrt%28+1052+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2810%29%2Bsqrt%28+1052+%29%29%2F2%5C2+=+5.60863737011343
x%5B2%5D+=+%28-%2810%29-sqrt%28+1052+%29%29%2F2%5C2+=+-10.6086373701134

Quadratic expression 2x%5E2%2B10x%2B-119 can be factored:
2x%5E2%2B10x%2B-119+=+2%28x-5.60863737011343%29%2A%28x--10.6086373701134%29
Again, the answer is: 5.60863737011343, -10.6086373701134. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B10%2Ax%2B-119+%29