Question

The length and breadth of a room are in the ratio of 3:2. Its height is equal to half of its length. If the cost of carpeting the floor at Rs 4.00 per sq. meter is Rs. 216, then the area of the four walls (in \[{m^2}\]) is
A 135
B 140
C 125
D 120

Answer 1

Hint: In this problem, first we need to find the length and breadth of the wall in one variable. Next, find the length and breadth of the wall using the given situation, and then find the height of the wall.

Complete step-by-step answer:
Consider, the length of the wall is \[3x\] and the breadth of the wall is\[2x\].
Now, the area of the floor is calculated as the product of length and breadth as shown below.
\[
  \,\,\,\,\,{\text{Area of floor}} = {\text{length}} \times {\text{breadth}} \\
   \Rightarrow {\text{Area of floor}} = 3x \times 2x \\
   \Rightarrow {\text{Area of floor}} = 6{x^2} \\
\]
Since, the cost of carpeting the floor at Rs 4.00 per sq. meter is Rs. 216, therefore,
\[
  \,\,\,\,\,6{x^2} \times 4 = 216 \\
   \Rightarrow 24{x^2} = 216 \\
   \Rightarrow {x^2} = \dfrac{{216}}{{24}} \\
   \Rightarrow {x^2} = 9 \\
   \Rightarrow x = 3 \\
\]
Therefore, the length and breadth of the wall is calculated as follows:
\[
  {\text{Length}} = 3\left( 3 \right) = 9m \\
  {\text{Breadth}} = 2\left( 3 \right) = 6m \\
\]
Since, the height of the wall is half of its length, therefore,
\[
  \,\,\,\,\,{\text{Height}} = \dfrac{{{\text{length}}}}{2} \\
   \Rightarrow {\text{Height}} = \dfrac{{\text{9}}}{2} \\
   \Rightarrow {\text{Height}} = 4.5m \\
\]
Now, the area of the four walls is calculated as follows:
\[
  \,\,\,\,\,\,\,{\text{Area of four walls}} = {\text{2}}\left( {{\text{length}} \times {\text{height + breadth}} \times {\text{height}}} \right) \\
   \Rightarrow {\text{Area of four walls}} = {\text{2}}\left( {{\text{9}} \times {\text{4}}{\text{.5 + 6}} \times {\text{4}}{\text{.5}}} \right) \\
   \Rightarrow {\text{Area of four walls}} = {\text{2}}\left( {{\text{40}}{\text{.5 + 27}}} \right) \\
   \Rightarrow {\text{Area of four walls}} = {\text{2}}\left( {{\text{67}}{\text{.5}}} \right) \\
   \Rightarrow {\text{Area of four walls}} = {\text{135}}{{\text{m}}^2} \\
\]
Thus, the area of the four walls is 135 sq. meters; hence, option (A) is the correct answer.

Note: Remembering the given formula in solution makes the problem easier to solve. In this problem, the area of the four walls is two times the sum of the product of length with height, and breadth with height.