Question

Two cross roads, each of width 5 m, run at right angles through the center of a rectangular park of length 70 m and breadth 45 m parallel to its sides. Find the area of the roads. Also, find the cost of constructing the roads at the rate of Rs 105 per m².

Answer 1

Let ABCD be the rectangular park then EFGH and IJKL are the two rectangular roads with width 5m.

Given that length of rectangular park = 70m

Breadth of rectangular park = 45m

Area of the rectangular park = Length x Breadth

= 70 m x 45 m

= 3150 m²

Area of the road EFGH = 70 m x 5 m

= 350 m²

Now, Area of the road JKIL = 45 m x 5 m

= 225 m²

From the figure, it is clear that area of MNOP is common to the two roads.

Thus, Area of MNOP = 5 m x 5 m = 25 m²

Therefore,

Area of the roads = Area of EFGH + Area of JKIL – Area of MNOP

= (350 + 225) m²– 25 m² 

= 550 m²

Again, it is given that the cost of constructing the roads = Rs. 105 per m²

Therefore,

Cost of constructing 550 m² area of the roads

= Rs. (105 x 550)

= Rs. 57750.