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 uncoverd. If the width of the carpet is 82 cm, find the cost at the rate of Rs 18 per metre.

Answer 1

We have,
Length of the hall PQ = 22 m and breadth of the hall QR = 15.5 m

∴ Area of the school hall PQRS = 22 m x 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 x 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
Again,
Area of the 1 m length of carpet = 1 m x 0.82 m = 0.82 m²
Thus,
Length of the carpet whose area is 287 m² = 287 m² ÷ 0.82 m² = 350 m
Cost of the 350 m long carpet = Rs. 18 x 350 = Rs. 6300