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Question
The length of verandah is 3m more than its breadth. The numerical value of its area is equal to the numerical value of its perimeter.
(i) Taking x, breadth of the verandah write an equation in ‘x’ that represents the above statement.
(ii) Solve the equation obtained in above and hence find the dimension of verandah.
Solution
Let breadth = xm, length = (x + 3)m.
Area = x (x + 3) sq.m.
Perimeter = 2(x + x + 3) = (4x + 6)m.
According to the question, x(x + 3) = 4x + 6
⇒ x2 - x - 6 = 0
⇒ (x + 2) (x ++ 3) = 0
∴ x = 3 and x = -2 (inadmissiable).
Hence breadth = 3m, length = 6m.
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