Question

A school has a hall $22m$ long and $15.5m$ wide , a carpet is laid inside the hall leaving around margin of $75cm$ from the walls. Find area of carpet and area of strip uncovered . If width of carpet is $82cm$ find its cost for $Rs.60$ per meter.

Answer 1

In rectangular hall,

Length $\left(L\right)=22m$

Breadth $\left(B\right)=15.5m$
The area of the hall $=L\times B$

$=22m\times 15.5m$

$=341m^2$
Margin of carpet $=75cm=75\times \frac{1}{100}m=0.75m$
[Since, $1cm=\frac{1}{100}$]

In carpet,

Length $\left(l\right)=22m-2\times 0.75m=22m-1.5m=20.5m$

Breadth $\left(b\right)=15.5m-2\times 0.75m=15.5m-1.5m=14m$

Area of the carpet $=l\times b=20.5m\times 14m=287m^2$
Area of uncovered portion $=341m^2-287m^2=54m^2$

Now, it is given that width of the carpet $=82cm=82\times \frac{1}{100}m=0.82m$

Since, Area of the carpet $=287m^2$

$\Rightarrow l\times b=287m^2$

$\Rightarrow l\times 0.82m=287m^2$

$\Rightarrow l=\frac{287m^2}{0.82m}$

$\Rightarrow l=287\times \frac{100}{82}m$

$\Rightarrow l=350m$

Cost of the carpet per meter $=Rs.60$

Cost of fencing the strip $=350\times Rs.60$
$=Rs.21000$