Question

A path 10 m wide runs around a square park of side 50 m. Find the area of the path. Also, find the cost of cementing it at the rate of Rs. 100 per 10 m${}^2$

Answer 1

Let PQRS be the square park of side 50 m. This shaded region represents the 10 m wide path.

Length of AB = 50 + (10+10) = 70 m

Area of the Square PQRS = (side)${}^2$ = (50 m)${}^2$ = 2500 m${}^2$

Area of the Square ABCD = (side)${}^2$ = (70 m)${}^2$ = 4900 m${}^2$

Therefore, Area of the path = (4900 -2500) = 2400 m${}^2$

Cost of cementing per 10 m${}^2$ = Rs. 100

Therefore, Cost of cementing 1 $m^2=Rs.10$

Thus, Cost of cementing 2400 $m^2=10\times 2400$

= Rs. 24000