Question

Is it possible to design a rectangular park of perimeter 80 m and area 400 m²? If so, find its length and breadth.

Answer 1

Length = l

Breadth = b

Perimeter = 2(L+b) = 80 

=> l+b = 40         .......... (eq 1)

Area = lb = 400 ........... (eq 2)

=> (l+b)² = (l-b)² + 4lb

=> 40² = (l-b)² + 4 x 400               [From eqn 1 & 2)

=> 1600 = (l-b)² + 1600

=> l-b = 0            .................... (eq 3)

                                L+b = 40

                                L-b =    0

                               2L = 40 => L = 20.

If L=20, then B=20 

So, yes ! We can construct a rectangular park of this length which is a square. Square is a Rectangle.