(Q12)Is it possible to design a rectangular park of perimeter 80 m and area 400 m2?If so, find its length and breadth.

Answer

Given: Perimeter of a rectangle 2(1 + b) = 80

6 + b =
80
2
 = 40

Area of the rectangle, l × b = 400

If possible, let us suppose that length of the rectangle = x m say

Then its breadth by equation (1) = 40 - x

By problem area = x.(40 - x) =

40x - x2=

x2 - 40x + = 0

Here a = 1; b = -40; c =

b2 - 4ac = (-40)2 - 4(1)()

= 1600 - = 0

The roots are real and equal.

They are
-b
2a
 ,
-b
2a

-(-40)
2 ×
=
40
 =

∴The dimensions are m,m.

(∴The park is in square shape)