Question

A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet? 19,200

Answer 1

2x+2y=5602x+2y=560 (perimeter) -->

x+y=280x+y=280

(2) x2+y2=2002x2+y2=2002 (diagonal, as per Pythagoras).

Question: xy=?xy=?

Square (1) -->

x2+2xy+y2=2802x2+2xy+y2=2802. Now

subtract (2) fro this: (x2+2xy+y2)−

(x2+y2)=2802−2002(x2+2xy+y2)−

(x2+y2)=2802−2002 --> 2xy=(280−200)

(280+200)2xy=(280−200)(280+200) -->

2xy=80∗4802xy=80∗480 -->

xy=40∗480=19200xy=40∗480=19200.