Area of 4 walls of a room is 108 sq meter. If height and length of room is in ratio 2:5 and height and breadth is in the ratio 4:5. Find the are of the floor of the room
h/L = 2/5, L = 2.5h.
h/W = 4/5, W = 1.25h.
2(h*L) + 2(h*W) = 108 m^2.
2(h*2.5h) + 2(h*1.25h) = 108,
5h^2 + 2.5h^2 = 108, h = 3.79 m.
A = L*W = 2.5h*1.25h = 2.5*3.79 * 1.25*3.79 = 45 m^2.
To find the area of the floor of the room, we need to determine the dimensions of the floor. Let's break down the given information and solve the problem step by step.
First, we are provided with the information that the area of the four walls of the room is 108 square meters. Since we know the area, we can express it as a sum of the areas of the individual walls.
Let's assume the length of the room is L, the height is H, and the breadth is B.
The area of the four walls of the room can be expressed as follows:
2 LH + 2 BH = 108
Now, we are given the ratios of the height and length (H:L) and the height and breadth (H:B). We can use these ratios to express the height and length, as well as the height and breadth, in terms of a common variable. Let's choose a variable, x, to represent the ratio.
Since H:L is given as 4:5, we can express the height as 4x and the length as 5x.
Similarly, since H:B is given as 4:5, we can express the height as 4x and the breadth as 5x.
Now, let's substitute these values into the equation for the area of the four walls:
2(5x)(4x) + 2(5x)(5x) = 108
Simplifying the equation:
40x^2 + 50x^2 = 108
90x^2 = 108
Now, divide both sides of the equation by 90 to isolate x^2:
x^2 = 108/90
x^2 = 1.2
Taking the square root of both sides of the equation:
x = √1.2
x ≈ 1.095
Now that we have the value of x, we can find the dimensions of the room.
Length (L) = 5x ≈ 5(1.095) ≈ 5.475 meters
Height (H) = 4x ≈ 4(1.095) ≈ 4.38 meters
Breadth (B) = 5x ≈ 5(1.095) ≈ 5.475 meters
Finally, to find the area of the floor, we multiply the length and breadth of the room:
Area of floor = L * B = 5.475 * 5.475 ≈ 29.97 square meters
Therefore, the area of the floor of the room is approximately 29.97 square meters.