SOLUTION: the perimeter of a rectangle plot is 68m and the length of its diagonal is 26m what is the area?

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Question 352018: the perimeter of a rectangle plot is 68m and the length of its diagonal is 26m what is the area?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Perimeter = P = 2L + 2W = 68
so L + W = 34, or
W = 34 - L.
The diagonal is 26, and so by the Pythagorean Theorem,
L%5E2%2BW%5E2=26%5E2
By direct substituion,
L%5E2+%2B+%2834-L%29%5E2=676
L%5E2+%2B1156-68L%2BL%5E2=676
2L%5E2-68L%2B480=0
L%5E2-34L%2B240=0
%28L-24%29%28L-10%29=0
This means L = 24, or L =10. Since we usually take the longer value value to be the length, L = 24, and from this W = 10.