Question

The cost of flooring a rectangular hall at $Rs.64$ per square meter is $Rs.2,048.$ If the breadth of the hall is $5m,$
find:
i. its length.
ii.its perimeter.
iii. cost of fixing a border of very small width along its boundary at the rate of $Rs.60$ per meter

Answer 1

Given,
The cost of flooring a rectangular hall at $Rs.64$ per square meter is $Rs.2,048.$
Area of the floor of the hall
$=\frac{\text{Cost of flooring}}{\text{Rate of flooring}}$
$=\frac{2048}{64}=\frac{256}{8}=32m^2$

We have,
Area $=32m^2$
Breadth $=5m$
The area of the floor of the rectangular is given by:
$A=\text{Length}\times \text{Breadth}$
$\Rightarrow 32=l\times 5$
$\therefore l=\frac{32}{5}=6.4m$

We have,
Length $=6.4m$
Breadth $=5m$
The perimeter of the floor of the rectangular hall is given by:
$P=2\left(\text{Length+Breadth}\right)$
$P=2(6.4+5)$
$P=2\left(11.4\right)$
$P=22.8m$

We have,
Perimeter $=22.8m$
Cost of fixing $=Rs.60$ per meter
Cost of fixing
$=\text{Perimeter}\times \text{Rate of fixing per meter}$
$=22.8\times 60=Rs.1,368$
Therefore, the cost of fixing is $Rs.1,368.$