SOLUTION: The diagonal of a rectangle platform is square root of 20 cm. If both dimensions are increased by 2 cm, then the resulting perimeter would be 5/3 of the original perimeter. Find th

Algebra ->  Rectangles -> SOLUTION: The diagonal of a rectangle platform is square root of 20 cm. If both dimensions are increased by 2 cm, then the resulting perimeter would be 5/3 of the original perimeter. Find th      Log On


   

Question 140784: The diagonal of a rectangle platform is square root of 20 cm. If both dimensions are increased by 2 cm, then the resulting perimeter would be 5/3 of the original perimeter. Find the dimensions of the rectangle.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
If the diagonal is sqrt%2820%29, then L%5E2%2BW%5E2=20, thank you Mr. Pythagoras.

The original perimeter is 2L+%2B+2W and the larger perimeter is 2%28L%2B2%29%2B2%28W%2B2%29, but the larger is 5/3 of the smaller so:


%285%2F3%29%282L+%2B+2W%29=2%28L%2B2%29%2B2%28W%2B2%29

5%282L+%2B+2W%29=6%28L%2B2%29%2B6%28W%2B2%29

10L%2B10W=6L%2B6W%2B24

4L%2B4W=24

L%2BW=6 or better for our purposes L=6-W

L%5E2%2BW%5E2=20
%286-W%29%5E2%2BW%5E2=20
36-12W%2BW%5E2%2BW%5E2-20=0
2W%5E2-12W%2B16=0
W%5E2-6W%2B8=0

Factors:
%28W-4%29%28W-2%29=0

So W = 4 or W = 2, meaning L = 2 or L = 4.

Check:
sqrt%284%5E2%2B2%5E2%29=sqrt%2816%2B4%29=sqrt%2820%29
2%284%29%2B2%282%29=8%2B4=12
12%2A%285%2F3%29+=+20

2%286%29%2B2%284%29=12%2B8=20 Checks.