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Question

The sides of a rectangular park are in the ratio 4 : 3. If its area is 1728 m2, find the cost of fencing it at Rs 30 per metre.

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Solution

Let the length of the field be 4x m.
Breadth = 3x m
∴ Area of the field = (4x × 3x) m2 = 12x2 m2
But it is given that the area is 1728 m2.
∴ 12x2 = 1728
⇒ x2 = 172812 = 144
⇒ x = 144 = 12
∴ Length = (4 × 12) m = 48 m
Breadth = (3 × 12) m =36 m
∴ Perimeter of the field = 2(l + b) units
= 2(48 + 36) m = (2 × 84) m = 168 m
∴ Cost of fencing = Rs (168 × 30) = Rs 5040

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