Question

A room is 15m long and 14m wide. A square carpet of 300 cm is laid on the floor. Find the area of the room which is not carpeted.

Answer 1

Hint: The area of the room floor is the product of length and breadth i.e., $a=l\times b$ where l is the length and b is the wideness of the floor. The area of the square carpet is $a^{\prime }=s^2$ where s is the side of the square carpet.

Complete step-by-step answer:
Given, the room is 15m and 14m wide.
Therefore, the Area of the floor of the room is $a=l\times b$ where, l is the length and b is the wideness of the floor.
$$\begin{gathered} \Rightarrow a=15\times 14 \\ \Rightarrow a=210m^2 \end{gathered}$$
Thus, the area of the room is $210m^2$.
And, The area of the carpet is $a^{\prime }=s^2$, where s is the side of the square carpet.
Given, side of the carpet is 300m
Since, $$\begin{gathered} 1m=100cm \\ \Rightarrow 300cm=3m \end{gathered}$$
Hence, the Side of the carpet in meters is $3m$
The area of the carpet will be
$$\begin{gathered} a^{\prime }=s^2 \\ \Rightarrow a^{\prime }=3^2=9m^2 \end{gathered}$$
Therefore, the area of carpet is $9m^2$i.e, the area of the room that is carpeted.
The area of the room which is not carpeted is the difference between the total area of the room and the area of the room which is carpeted.
$$\begin{gathered} \Rightarrow a-a^{\prime } \\ \Rightarrow (210-9)m^2=201m^2 \end{gathered}$$
 Hence, The Area of the room which is not carpeted is $210m^2$

Note: Important aspect to notice and keep in mind is the side of the carpet is given in centimeters and the rest values are given in meters. So, we must change every value in the same metric system. We, therefore, changed the value of the side of the carpet into meters from centimeters.