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?

Answer 1

Answer with Step-by-step explanation:

Let l denotes the length of rectangle

and b denotes its breath.

Then, Perimeter=2(l+b)

Diagonal=$\sqrt{l^2+b^2}$

and Area=lb

Perimeter=560 feet

i.e. 2(l+b)=560

(l+b)=280    (on dividing both sides by 2)

Diagonal=200 feet

i.e. $\sqrt{l^2+b^2}=200$

l²+b²=40000   (on squaring both sides of above equation)

Also (l+b)=280

On squaring this, we get

l²+b²+2lb=78400

40000+2lb=78400

2lb=78400-40000

2lb=38400

lb=19200    (on dividing both sides by 2)

Hence, Area of rectangular park is:

19200 square feet