What is the amount required to construct a 3 m wide path around a rectangular park of 50 m length and 30 m width at the rate of Rs 500 per square metre?

Let ABCD be the rectangular park such that length AB = 50 m and width BC = 30 m.

The path that is to be constructed around the park is represented by the shaded portion.

It is clearly seen that,

Area of the path = area of rectangle EFGH − an area of rectangle ABCD

Length of the rectangle EFGH = EF = 50 m + 3 m + 3 m = 56 m

Breadth of the rectangle EFGH = 30 m + 3 m + 3 m = 36 m

Area of rectangle EFGH = length × breadth = 56 m × 36 m = 2016 m²

Area of rectangle ABCD = length × breadth = 50 m × 30 m = 1500 m²

Therefore, the area of the path = 2016 − 1500 = 516 m²

The cost of constructing 1 m² of the path is Rs 500.

Thus, the total amount required for constructing the path = Rs 500 × 516 = Rs 2,58,000.