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 the park has an area 305 m². Find the dimensiions of the park.

Answer 1

We have,
Area of the path = 305 m²

Let the length of the park be 5x m and the breadth of the park be 2x m
Thus,
Area of the rectangular park = 5x x 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) m x (2x + 5) m = (10x² + 25x + 10x + 25) m²= (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
Therefore,
Length of the park = 5x = 5 x 8 = 40 m
Breadth of the park = 2x = 2 x 8 = 16 m