Question

The length of a rectangular verandah is 3 m more than its breadth. The numerical value of its area is equal to the numerical value of its perimeter.

(i) Taking x as the breadth of the verandah, write an equation in x that represents the above statement

(ii) Solve the equation obtained in (i) above and hence find the dimensions of the verandah. 

Answer 1

(i) The breadth of the verandah = x
Length of the verandah = x + 3
According to the question

2( x + ( x + 3 )) = x ( x + 3)
4x + 6 = x² + 3x 
x² - x - 6 = 0

(ii) From the above equation
           x² - x - 6 = 0
( x - 3 ) ( x + 2 ) = 0
                      x = 3
Hence breadth = 3m
Length = 3 + 3 = 6m