Question

A‌ ‌room‌ ‌is‌ ‌\[13\,m\]‌ ‌long‌ ‌and‌ ‌$9\,m$‌ ‌broad.‌ ‌Find‌ ‌the‌ ‌cost‌ ‌of‌ ‌carpeting‌ ‌the‌ ‌room‌ ‌with‌ ‌a‌ ‌carpet‌ ‌\[75\,cm\]‌ ‌broad‌ ‌at‌ ‌the‌ ‌rate‌ ‌of‌ ‌Rupees‌ ‌\[65\]‌ ‌per‌ ‌meter.‌

Answer 1

Hint: The given question deals with finding the cost of carpeting the room and can be done by using some units and measurement formulas such as area of rectangle which is calculated by multiplying its length into its breadth. Basic units conversion rules must be kept in mind while doing the given problem.

Complete step-by-step solution:

Given
Length of the room $ = 13m$
Breadth of the room $ = 9m$
Area of the room $ = \text{length} \times \text{breadth}$
$= (13 \times 9){m^2}$
$= 117\,{m^2}$
Let the length required of the carpet be $x\,m$
Breadth of the carpet \[ = 75cm\]
Convert \[75cm\] into m as all the dimensions are in meters. Divide \[75\] by \[100\]. We get,
Breadth of the carpet \[ = 0.75m\]
So area of the carpet $ = (0.75 \times x)\,{m^2}$$ = 0.75x\,{m^2}$
For carpeting the room
Area converted by the carpet $ = $ Area of the room
$0.75x = 117$
$\Rightarrow x = \dfrac{{117}}{{0.75}}$
$\Rightarrow x = 156m$
Hence length of the carpet $ = 156m$
$1m$ carpet cost $ = $\[65Rs.\]
The cost of \[156m\] carpet will be $ = 156 \times 65$\[ = Rs\,10140\]
Hence the cost of carpeting the room is \[10140\] Rupees.

Note: Generally the area is the region occupied by the thing. The area of a rectangle is defined as the region occupied by the quadrilateral region. We must know the formulae for area and perimeter of basic shapes like square, rectangle, parallelogram, circle, etc. We also must take care of the calculations while doing such questions. The method that we have followed in the given question to find the cost of carpeting given the rate per square metre is called the unitary method.