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.

Answer 1

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