Question

find the height of a room 15m long and 10m wide,the area of whose floor and ceiling together is equal to area of 4 walls.​

Answer 1

To determine the height of a room given the area of the floor and ceiling equals the area of the 4 walls, the height is found by dividing the combined area of the floor and ceiling by the perimeter of the room. Based on the given dimensions, the height of the room is calculated to be 6 meters.

Step-by-step explanation:

To find the height of a room that is 15m long and 10m wide, where the area of the floor and ceiling combined is equal to the area of the 4 walls, we need to use the formula for the surface area of the walls and compare it to the combined area of the floor and ceiling.

First, calculate the area of the floor and the ceiling:

• Area of floor or ceiling = length × width
• Area of floor or ceiling = 15m × 10m = 150m²
• Combined area of floor and ceiling = 2 × 150m² = 300m²

Next, express the area of the walls in terms of the height h:

• Area of walls = 2 × (length + width) × height
• Area of walls = 2 × (15m + 10m) × h = 2 × 25m × h = 50m × h

Since the area of the floor and ceiling together is equal to the area of the 4 walls:

1. 300m² = 50m × h
2. h = 300m² / 50m
3. h = 6m
4. The height of the room is therefore 6 meters.