Question

A rectangular hall is $22m$ long and $15.5m$ broad. A carpet is to be laid inside the hall leaving all around a margin of $75cm$ from the walls. Find the area of the carpet and area of the strip left uncovered. If the width of the carpet is $82cm,$ find its cost at the rate of $Rs.124$ per metre.

Answer 1

Length of the rectangular hall, $l=22m$ and Breadth, $b=15.5m$

The area of the rectangular hall $=l\times b=22\times 15.5=341m^2$

Margin of carpet $=75cm=0.75m$

Area of carpet (rectangular) $=(22-2\times 0.75)\times (15.5-2\times 0.75)$

$=(22-1.5)(15.5-1.5)$

$=20.5\times 14=287m^2$

Area of the carpet $=287m^2$

Portion uncovered (Area of strip uncovered) $=$ Area of rectangular hall $-$ Area of the carpet

=$341-287=54m^2$

Width of the carpet $=82cm=0.82m$

Length of carpet required $=\frac{\text{Total Area of carpet}}{\text{Width of carpet}}$

$=\frac{287}{0.82}=350m$

Cost of $1m$ length carpet $=Rs.124$

Total cost of $350m$ length of carpet $=350\times 124=Rs.43400$