Question

The length and breadth of a rectangular park are in the ratio 5 : 2. A 2.5-m-wide path running all around the outside of the aprk has an area of 305 m². Find the dimensions of the park.

Answer 1

Area of the path = 305 m²

Let the length of the park be 5x m and the breadth of the park be 2x m.

∴ Area of the rectangular park = 5x $\times$ 2x = 10x² m²
Width of the path = 2.5 m
Outer length, PQ = 5x m + 2.5 m + 2.5 m = (5x + 5) m
Outer breadth, QR = 2x + 2.5 m + 2.5 m = (2x + 5) m
Area of PQRS = (5x + 5) $\times$ (2x + 5) = (10x² + 25x + 10x + 25) = (10x² + 35x + 25) m²
∴ Area of the path = [(10x² + 35x + 25) − 10x² ] m²
⇒ 305 = 35x + 25
⇒ 305 − 25 = 35x
⇒ 280 = 35x
⇒ x = 280 ÷ 35 = 8

∴ Length of the park = 5x = 5 $\times$ 8 = 40 m
Breadth of the park = 2x = 2 $\times$ 8 = 16 m