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

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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) About Me  (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 ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B4x%2B-320+=+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=%284%29%5E2-4%2A2%2A-320=2576.

Discriminant d=2576 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+2576+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+2576+%29%29%2F2%5C2+=+11.6885775404495
x%5B2%5D+=+%28-%284%29-sqrt%28+2576+%29%29%2F2%5C2+=+-13.6885775404495

Quadratic expression 2x%5E2%2B4x%2B-320 can be factored:
2x%5E2%2B4x%2B-320+=+2%28x-11.6885775404495%29%2A%28x--13.6885775404495%29
Again, the answer is: 11.6885775404495, -13.6885775404495. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B4%2Ax%2B-320+%29


Thus it is roughly 11.69 x 13.69