Question

A rectangular field is of dimension 20 m × 15 m. Two paths run parallel to the sides of the rectangle through the centre of the field. The width of the longer path is 2 m and that of the shorter path is 1 m. Find (i) the area of the paths (ii) the area of the remaining portion of the field (iii) the cost of constructing the roads at the rate of ₹ 10 per sq.m

Answer 1

Length of the rectangular field L = 20 m

Breadth B = 15 m

Area = L × B

= 20 × 15 m²

Area of outer rectangle = 300 m² 

Area of inner small rectangle = `19/2 xx 13/2` = 61.75 cm²  

(i) Area of the path = Area of the outer rectangle – Area of 4 inner small rectangles

= 300 – 4(61.75)

= 300 – 247

= 53 m²

Area of the paths = 53 m²

(ii) Area of the remaining portion of the field

= Area of the outer rectangle – Area of the paths

= 300 – 53 m² 

= 247 m²

Area of the remaining portion = 247 m²

(iii) Cost of constructing 1 m² road = ₹ 10

∴ Cost of constructing 53 m² road = ₹ 10 × 53 = ₹ 530

∴ Cost of constructing road = ₹ 530