Question

The length and breadth of a rectangular park are in the ratio 8:5. A path 1.5 m wide running all round the outside of the park has an area of 594 m^₂. Find the dimensions of the park.

Answer 1

Let PQRS be the rectangular park of length 8x m and breadth 5x m. The width of the path outside it is 1.5 m.



Length of the rectangle ABCD = AB = (8x + 1.5 + 1.5) m = (8x + 3) m
Its breadth = BC = (5x + 1.5 + 1.5) m = (5x + 3) m
Area of ABCD = AB × BC
= (8x + 3) × (5x + 3) m²
= (40x² + 24x + 15x + 9) m²
= (40x² + 39x + 9) m²

Area of rectangle PQRS = PQ × QR
= (8x) × (5x) m²
= 40x² m²

Area of the path = area of ABCD − area of PQRS
$\Rightarrow$ 594 = 40x² + 39x + 9 - 40x²
$\Rightarrow$ 594 = 39x + 9
$\Rightarrow$ 39x = 585
$\Rightarrow$ x = 15
∴ Length of the rectangular park = 8x m= 8 × 15 m = 120 m
and its breadth = 5x m= 5 × 15 m = 75 m