Question

A rectangle has an area of 36 cm and perimeter of 30cm Find the larger side of it.

Answer 1

Let Larger( length ) side be ( x cm ) and Shorter side be ( 36 / x )

Given, Perimeter = 30

2( length + breadth ) = 30

=> x + ( 36 / x ) = 15

=> ( x^2 + 36 ) / x = 15

=> x^2 + 36 = 15x

=> x^2 - 15x + 36 = 0

=> x^2 - ( 12 + 3 ) x + 36 = 0

=> x^2 - 12x - 3x + 36 = 0

=> x( x - 12 ) - 3( x - 12 ) = 0

=> ( x - 12 ) ( x - 3 ) = 0

=> x - 12 = 0 Or x - 3 = 0

=> x = 12 Or x = 3

Hence, x = 12 cm [ Taking larger one ]

Larger side = x = 12 cm