A room 15 m long requires 7500 tiles, each 15 cm by 12 cm, to cover the entire floor, then the breadth of the room is :

Question

Accepted Answer

To determine the breadth of the room, we need to calculate the total area of the floor covered by the tiles and then use this information to find the breadth.

1. **Calculate the area covered by one tile:**
   - Each tile measures 15 cm by 12 cm.
   - The area of one tile = 15 cm × 12 cm = 180 square centimeters.

2. **Calculate the total area covered by all tiles:**
   - The room requires 7500 tiles to cover the entire floor.
   - Total area covered by tiles = 7500 tiles × 180 square centimeters per tile = 1,350,000 square centimeters.

3. **Convert the total area from square centimeters to square meters:**
   - Since 1 square meter = 10,000 square centimeters, we convert the total area:
   - Total area in square meters = 1,350,000 square centimeters ÷ 10,000 = 135 square meters.

4. **Use the area to find the breadth of the room:**
   - We know the length of the room is 15 meters.
   - Area of the room = Length × Breadth
   - 135 square meters = 15 meters × Breadth
   - Breadth = 135 square meters ÷ 15 meters = 9 meters.

Therefore, the breadth of the room is 9 meters, which corresponds to Option 2.

**Explanation for why other options are incorrect:**

- **Option 1 (7 m):** If the breadth were 7 meters, the area of the room would be 15 meters × 7 meters = 105 square meters, which is less than the calculated area of 135 square meters. Therefore, this option is incorrect.

- **Option 3 (13 m):** If the breadth were 13 meters, the area of the room would be 15 meters × 13 meters = 195 square meters, which is more than the calculated area of 135 square meters. Therefore, this option is incorrect.

- **Option 4 (17 m):** If the breadth were 17 meters, the area of the room would be 15 meters × 17 meters = 255 square meters, which is significantly more than the calculated area of 135 square meters. Therefore, this option is incorrect.

In conclusion, the correct breadth of the room is 9 meters, making Option 2 the correct choice.