Question

A school has a hall which is 22 m long and 15.5 m broad. A carpet is laid inside the hall leaving all around a margin of 75 cm from the walls. Find the area of the carpet and the area of the strip left uncovered. If the width of the carpet is 82 cm, find its cost at the rate of Rs 60 per m.

Answer 1

Length of the hall, PQ = 22 m
Breadth of the hall, QR = 15.5 m

∴ Area of the school hall PQRS = 22 m $\times$ 15.5 m = 341 m²
Length of the carpet, AB = 22 m − ( 0.75 m + 0.75 m) = 20.5 m [since 100 cm = 1 m]
Breadth of the carpet, BC = 15.5 m − ( 0.75 m + 0.75 m) = 14 m
∴ Area of the carpet ABCD = 20.5 m $\times$ 14 m = 287 m²
Area of the strip = Area of the school hall (PQRS) − Area of the carpet (ABCD)
= 341 m² − 287 m²
= 54 m²

Area of 1 m length of the carpet = 1 m $\times$ 0.82 m = 0.82 m²

∴ Length of the carpet whose area is 287 m² = 287 m² ÷ 0.82 m² = 350 m
Cost of the 350 m long carpet = Rs 60 $\times$ 350 = Rs 21000