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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.
Solution
(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
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