SOLUTION: the perimeter of a rectangle is 34 m and the diagonal is 13 m. find the dimensions and calculate the area.

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Question 250625: the perimeter of a rectangle is 34 m and the diagonal is 13 m. find the dimensions and calculate the area.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
2L%2B2W=34
1.L%2BW=17
2.L%5E2%2BW%5E2=13%5E2
From 1,
L=17-W
L%5E2=289-34W%2BW%5E2
Subsitute into 2,
L%5E2%2BW%5E2=13%5E2
289-34W%2BW%5E2%2BW%5E2=13%5E2
2W%5E2-34W%2B289=169
2W%5E2-34W%2B120=0
%282W-10%29%28W-12%29=0
Two solutions:
2W-10=0
2W=10
W=5
Then
L%2BW=17
L=12
.
.
.
The second solution is
W-12=0
W=12
L=5
.
.
.
The area of the rectangle is
A=LW=%285%29%2812%29=60+m%5E2