Area of the four walls of a room is 108 m2. If the height and length of the room are in the ratio of 2 : 5 and the height and breadth in the ratio 4 : 5, then the area, in m2, of the floor of the room is :
ratio of
height : length = 2 : 5 = 2x : 5x = 4x : 10x
ratio of height : breadth (width ?) = 4 : 5 = 4x : 5x
height : length : width = 4x : 10x : 5x
area = 2(lh) + 2(wh)
= 2(10x)(4x) + 2(5x)(4x) = 108
120x^2 = 108
x^2 = .9
floor is 10x by 5x = 25x^2 = 25(.9) = 22.5 m^2
80',80',100',100'
A room is 12 m long,8m wide,4m high. What is the area of four walls?
Options- 80sq. Metres
284sq. Metres
160sq. Metres
144sq. Metre
To find the area of the floor of the room, we need to determine the dimensions of the room based on the given ratios.
Let's assume the height of the room is 2x, the length is 5x, and the breadth is 5y. We can use the ratio of height and length to find the value of x:
2x / 5x = 4 / 5
Cross-multiplying, we get:
(2x)(5) = (5x)(4)
10x = 20x
10x - 20x = 0
-10x = 0
x = 0
From this, we can see that x is equal to 0. However, this does not make sense in the context of the problem as we cannot have a room with no height. Therefore, we made a mistake in assuming the ratios.
Let's try a different approach:
Assume the height of the room is 4x and the breadth is 5y. We can use the ratio of height and breadth to find the value of y:
4x / 5y = 2 / 5
Cross-multiplying, we get:
(4x)(5) = (5y)(2)
20x = 10y
20x - 10y = 0
10(2x - y) = 0
From this, we can see that 2x - y = 0
Simplifying further, we have:
2x = y
Now, we can substitute this value of y back into the equation for the area of the four walls:
2(length + breadth) x height = 108 m²
2((5x) + (5(2x))) x 4x = 108
2(5x + 10x) x 4x = 108
2(15x) x 4x = 108
30x x 4x = 108
120x² = 108
Now, we can solve this equation to find the value of x:
x² = 108 / 120
x² = 9 / 10
x = √(9 / 10)
x = 3 / √10
Now that we have the value of x, we can substitute it back into the equation for the area of the four walls to find the value of the length:
Length = 5x = 5 * (3 / √10) = (15 / √10)
Similarly, we can find the value of the breadth:
Breadth = 5y = 5 * (2x) = 5 * (2 * (3 / √10)) = (30 / √10)
Now that we have the dimensions of the room, we can find the area of the floor:
Area of floor = Length x Breadth
Area of floor = (15 / √10) x (30 / √10)
Area of floor = (15 * 30) / (√10 * √10)
Area of floor = 450 / 10
Area of floor = 45 m²
Therefore, the area of the floor of the room is 45 m².