Is it possible to design a rectangular park of perimeter 80 m and area

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

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

Answer»

Solution:

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.