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Question
The length of a rectangular garden is 12 m more than its breadth. The numerical value of its area is equal to 4 times the numerical value of its perimeter. Find the dimensions of the garden.
Solution
Let breadth = x m
then length = (x + 12) m
Area = l × b = x (x + 12) m2
and perimeter
= 2(l + b)
= 2(x + 12 + x)
= 2 (2x + 12) m
According to the condition.
x(x + 12) = 4 x 2(2x + 12)
⇒ x2 + 12x = 16x + 96
⇒ x2 + 12x - 16x - 96 = 0
⇒ x2 - 4x - 96 = 0
⇒ x2 - 12x + 8x - 96 = 0
⇒ x(x - 12) + 8(x - 12) = 0
⇒ (x - 12)(x + 8) = 0
Either x - 12 = 0,
then x = 12
or
x + 8 = 0,
then x = -8,
but it is not possible as it is in negative.
∴ Breadth = 12m
and length = 12 + 12 = 24m.
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