(Q9)Find the dimensions of the rectangle whose perimeter is 28 meters and whose area is 40 square meters.

Answer

Let the length of the rectangle = x

Given perimeter = 2(1 + b) = 28

(1 + b)=
28
2
 = 14

Breadth of the rectangle = 14 - x

Area = length.breadth = x(14 - x) = 14x - x2

By problem 14x - x2 = 40

x2 - 14x + 40 = 0

x2 - x - 4x + 40 = 0

x(x - ) - 4(x-) = 0

(x - )(x - 4) = 0

x - = 0(or)x - 4 = 0

x = (or) 4

∴Length= m or 4 m

The breadth = 14 - = m (or) 14 - 4 = 10 m