SOLUTION: The length of the diagonal of a rectangle is 5ft. The rectangle’s perimeter is 13 ft. find the rectangle’s dimensions.

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Question 733531: The length of the diagonal of a rectangle is 5ft. The rectangle’s perimeter is 13 ft. find the rectangle’s dimensions.
Found 2 solutions by richwmiller, Alan3354:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
a^2+b^2=5,
2*(a+b)=13
no solution
Something is wrong with the problem

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The length of the diagonal of a rectangle is 5ft. The rectangle’s perimeter is 13 ft. find the rectangle’s dimensions.
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L%5E2+%2B+W%5E2+=+25
2L + 2W = 13 --> L + W = 6.5 --> W = 6.5 - L
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Sub for W in the 1st eqn
L%5E2+%2B+W%5E2+=+25
L%5E2+%2B+%286.5+-+L%29%5E2+=+25
2L%5E2+-+13L+%2B+17.25+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-13x%2B17.25+=+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=%28-13%29%5E2-4%2A2%2A17.25=31.

Discriminant d=31 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--13%2B-sqrt%28+31+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-13%29%2Bsqrt%28+31+%29%29%2F2%5C2+=+4.64194109070751
x%5B2%5D+=+%28-%28-13%29-sqrt%28+31+%29%29%2F2%5C2+=+1.85805890929249

Quadratic expression 2x%5E2%2B-13x%2B17.25 can be factored:
2x%5E2%2B-13x%2B17.25+=+%28x-4.64194109070751%29%2A%28x-1.85805890929249%29
Again, the answer is: 4.64194109070751, 1.85805890929249. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-13%2Ax%2B17.25+%29

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The 2 solutions are L & W.