SOLUTION: a rectangle with perimeter 16 has a diagonal of 2radical10. find the length of the longer side of the rectangle

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Question 944377: a rectangle with perimeter 16 has a diagonal of 2radical10. find the length of the longer side of the rectangle
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
P=2%28L%2BW%29=16
L%2BW=8
and
L%5E2%2BW%5E2=%282sqrt%2810%29%29%5E2
L%5E2%2BW%5E2=40
From eq. 1,
L=8-W
L%5E2=%288-W%29%5E2
L%5E2=64-16W%2BW%5E2
Substituting,
64-16W%2BW%5E2%2BW%5E2=40
2W%5E2-16W%2B24=0
W%5E2-8W%2B12=0
%28W-6%29%28W-2%29=0
So then,
W-6=0
W=6
Then,
L=8-6
L=2
and
W-2=0
W=2
and
L=8-2
L=6
The rectangle is 6 x 2.