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 140787: 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 Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let call the length and width of the rectangle L and W.
1.L%5E2%2BW%5E2=20
The original perimeter is 2L+2W.
2.2%28L%2B2%29%2B2%28W%2B2%29=%285%2F3%29%282L%2B2W%29
Simplifying 2 (multiply both sides by 3 to get rid of denominators),
6%28L%2B2%29%2B6%28W%2B2%29=5%282L%2B2W%29
6L%2B12%2B6W%2B12=10L%2B10W
4L%2B4W=24
L%2BW=6
L=6-W
Now plug this value into 1.
1.L%5E2%2BW%5E2=20
%286-W%29%5E2%2BW%5E2=20
%2836-12W%2BW%5E2%29%2BW%5E2=20
2W%5E2-12W%2B36=20
2W%5E2-12W%2B16=0
W%5E2-6W%2B8=0
%28W-4%29%28W-2%29=0
The two solutions are W=4 and W=2.
For W=4, L=6-W=2.
For W=2, L=6-W=4.
The dimensions of the rectangle are 2 cm by 4 cm.