Question

Is it possible to design a rectangular park of perimeter 80m and area $400m^2$? If so, find its length and breadth.

Answer 1

Let the length and breadth of the park be L and b.
Perimeter =$2(L+b)=80$
$L+b=40$
Or, $b=40-L$

Area = $L\times b=L(40-L)$ = $40L-L^2=400$

$=L^2-40L+400$
$=(L-20{)}^2$

Therefore, length of park, $L=20m$
And breadth of park, $b=40-L=40-20=20m.$
Since the length = breadth, the park is in the shape of a square, which is also a rectangle.