Problem Solving

A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet?

A. 19,200
B. 19,600
C. 20,000
D. 20,400
E. 20,800


2x+2y = 560

x^2 + y^2 =200
x+y=10sqrt2

so,
2x+2(10sqrt2 -x)=560
then
x becomes 0...

Can anyone explain where did I do wrong?

dunkin77 wrote:
2x+2y = 560

x^2 + y^2 =200
x+y=10sqrt2

so,
2x+2(10sqrt2 -x)=560
then
x becomes 0...

Can anyone explain where did I do wrong?

This should read as
x^2 + y^2 =40000
since the diagonal is Root of Sum of Squares of the two sides.(Pythagoras Theorem)

Oops, thank you.

but still if I substitute..

2x+2(200-x) = 560

x get zero...

dunkin77 wrote:A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet?

A. 19,200
B. 19,600
C. 20,000
D. 20,400
E. 20,800


2x+2y = 560

x^2 + y^2 =200
x+y=10sqrt2

x+y = 280
x^2 + y^2 =40000
(X+y)^2 = x^2 +y^2 +2xy

(280)^2 -(200)^2 = 2xy
480 x80 = 2xy
xy = 240x80 = 19200