SOLUTION: 37.) Show a complete solution to the problem. If the perimeter of a rectangle is 20 feet and the diagonal is 2 squrt(13) feet then what are the length and width?

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Question 165185: 37.) Show a complete solution to the problem.
If the perimeter of a rectangle is 20 feet and the diagonal is 2 squrt(13) feet then what are the length and width?

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
37.) Show a complete solution to the problem.
If the perimeter of a rectangle is 20 feet and the diagonal is 2 squrt(13) feet then what are the length and width?
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Perimeter = 2L + 2W = 20
Area = L*W
D+=+SQRT%28L%5E2+%2B+W%5E2%29 = 2sqrt%2813%29
2L + 2W = 20
L + W = 10
W = 10-L
Sub into the other eqn
sqrt%28L%5E2+%2B%2810-L%29%5E2%29+=+2sqrt%2813%29
Square both sides
L^2 + (10-L)^2 = 4*13
L%5E2+%2B+L%5E2+-+20L+%2B+100+=+52
2L%5E2+-+20L+%2B+48+=+0
L%5E2+-+10L+%2B+24+=+0
(L-6)*(L-4)=0
L = 6, L= 4
If L=6, W=4
If L=4, W=6