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)   (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)   (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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2L + 2W = 13 --> L + W = 6.5 --> W = 6.5 - L
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Sub for W in the 1st eqn



Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
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=31 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 4.64194109070751, 1.85805890929249. Here's your graph:

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The 2 solutions are L & W.
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