If the area of the walls of a room is [tex]$72 m^2$[/tex], its length is 8 m, and its breadth is 4 m, what is its height?
Answer (2)
Define the variables: area A , length l , breadth b , and height h .
Use the formula for the area of the walls: A = 2 h ( l + b ) .
Substitute the given values: 72 = 2 h ( 8 + 4 ) .
Solve for the height: h = 24 72 = 3 .
The height of the room is 3 m .
Explanation
Problem Analysis We are given the area of the walls of a room, its length, and its breadth. We need to find the height of the room. Let's denote the area of the walls as A , the length as l , the breadth as b , and the height as h .
Formula The formula for the area of the walls of a room is given by: A = 2 h ( l + b ) where A is the area of the walls, h is the height, l is the length, and b is the breadth of the room.
Substitution We are given that the area of the walls is A = 72 m 2 , the length is l = 8 m , and the breadth is b = 4 m . Substituting these values into the formula, we get: 72 = 2 h ( 8 + 4 ) 72 = 2 h ( 12 ) 72 = 24 h
Solving for h Now, we solve for h :
h = 24 72 h = 3
Final Answer Therefore, the height of the room is 3 meters.
Examples
Understanding how to calculate the height of a room given its wall area, length, and breadth is useful in various real-life scenarios. For example, when estimating the cost of painting a room, you need to know the area of the walls. If you know the length, breadth, and wall area, you can calculate the height to determine the volume of paint required. This also applies to installing wallpaper or other wall coverings, ensuring you purchase the correct amount of materials. Knowing the dimensions of a room is also crucial in interior design for furniture placement and overall space planning. The formula A = 2 h ( l + b ) helps in these practical applications.
The height of the room is 3 meters, calculated using the formula for the area of the walls. We substituted the given length and breadth into the formula and solved for the height. Thus, h = 3 m .
;
