SOLUTION: the diagonal of a rectangle is 15cm, and the perimeter is 38cm. What is the area? Is it possible to find the answer without finding the dimensions of the rectangle?

Algebra ->  Rectangles -> SOLUTION: the diagonal of a rectangle is 15cm, and the perimeter is 38cm. What is the area? Is it possible to find the answer without finding the dimensions of the rectangle?      Log On


   

Question 359713: the diagonal of a rectangle is 15cm, and the perimeter is 38cm. What is the area? Is it possible to find the answer without finding the dimensions of the rectangle?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let's see.
D%5E2=L%5E2%2BW%5E2
.
.
P=2L%2B2W=2%28L%2BW%29=38
L%2BW=19
.
.
%28L%2BW%29%5E2=L%5E2%2B2LW%2BW%5E2
%28L%2BW%29%5E2=%28L%5E2%2BW%5E2%29%2B2LW
%28L%2BW%29%5E2=%28D%5E2%29%2B2LW
D%5E2%2B2LW=19%5E2
.
.
15%5E2%2B2LW=19%5E2
225%2B2LW=361
2LW=136
LW=68
It just happens that LW is also the area of a rectangle.
highlight%28A=68%29cm^2