Question

A rectangular lawn 70 m by 50 m has two roads, each 5 m wide, running through its middle, one parallel to its length and the other parallel to its breadth. Find the cost of constructing the roads at Rs 120 per m².

Answer 1

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

Length of the rectangular park, AD = 70 m
Breadth of the rectangular park, CD = 50 m
∴ Area of the rectangular park = Length $\times$ Breadth = 70 m $\times$ 50 m = 3500 m²
Area of road EFGH = 70 m $\times$ 5 m = 350 m²
Area of road IJKL = 50 m $\times$ 5 m = 250 m²

Clearly, area of MNOP is common to both the two roads.

∴ Area of MNOP = 5 m $\times$ 5 m = 25 m²

Area of the roads = Area (EFGH) + Area (IJKL) − Area (MNOP)
= (350 + 250 ) m²− 25 m² = 575 m²
It is given that the cost of constructing the roads is Rs. 120/m².

Cost of constructing 575 m² area of the roads = Rs. (120 × 575)
= Rs. 69000