Question

A rectangular grassy plot is 75 m long and 60 m broad. If has path of width 2 m all around it on the inside. Find the area of the path and cost and of constructing it at Rs 125 per m².

Answer 1

Let PQRS be the given grassy plot and ABCD be the inside boundary of the path.

Length = 75 m
Breadth = 60 m
Area of the plot = (75 $\times$ 60) m² = 4500 m²
Width of the path = 2 m
∴ AB = (75 - 2 $\times$ 2) m = (75 - 4) m =71 m
AD = (60 - 2 $\times$ 2) m = (60 - 4) m = 56 m
Area of rectangle ABCD = (71 x 56) m² = 3976 m²
Area of the path = (Area of PQRS - Area of ABCD)
= (4500 - 3976) m² = 524 m²
Rate of constructing the path = Rs 125 per m²
∴ Total cost of constructing the path = Rs (524 $\times$ 125) = Rs 65,500