Question

Two cross roads, each of width 4 m, run at right angles through the centre of a rectangular park of length 60 m and breadth 40 m and parallel to its sides. Find the area of the roads. Also find the cost of constructing the roads at the rate of ₹ 100 sq.m.

Answer 1

Length of the rectangular park = 60 m 

Breadth of the rectangular park = 40 m 

Length of the path along length of the park = 60 m 

Width of the path along length of the park = 40 m 

Area of the path along length of the park = 60 × 4 = 240 m² 

Similarly, 

Length of the path along breadth of the park = 40 m 

Width = 4m

∴ Area of the path along its breadth = 40 × 4 = 160 m² 

Hence, area of the paths = Area of the path along length + Area of the path along breadth – Area of the intersecting square 

= 240 + 160 – 4 × 4 

= 400 – 16 = 384 

∴ Cost of construction at the rate of ₹ 100 per sq.m = 384 × 100 = ₹ 38400