# Area of the four walls of a room is 108m^{2}. 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 m^{2} of the floor of the room is: (1) 72 (2) 54 (3) 45 (4) 24

Area of the four walls of a room can be calculated by finding the lateral surface area of a cuboid.

## Answer: The area of the floor of a room whose height and length are in the ratio of 2 : 5, and the height and breadth are in the ratio 4: 5, is 45 m^{2}.

Let's find the area of the floor of the room.

**Explanation:**

Let length, breadth, and the height of the room be l, b, and h

Given:

h : l = 2 : 5

h : b = 4 : 5

By multiplying h : l with 2 to get equal parts of h in both the ratios we get,

h : l = 4 : 10

Also,

h : b = 4 : 5

Thus, h : l : b = 4 : 10 : 5

Let's assume h, l and b as 4x, 10x and 5x (Since, h : l : b = 4 : 10 : 5)

Area of the four walls = 2hb + 2hl = 2h(l + b) = 108

=> Area of the four walls = 2 × 4x(10x + 5x) = 108

2 × 60x^{2} = 108

x^{2} = 108/120 = 9/10

The area of the floor = l × b

Thus, area of the floor = 10x × 5x = 50x^{2}

The area of the floor = 50 × (9/10) (Since, x^{2} = 9/10)

Hence, the area of the floor = 45 m^{2}

### Thus, Option (3) 45 is the area in m^{2} of the floor of a room whose height and length are in the ratio of 2 : 5 and the height and breadth are in the ratio 4 : 5.

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