The length, breadth and height of a room are 6 m 25 cm, 8 m 75 cm and 5 m 50 cm, respectively, Determine the longest rod which can measure the three dimensions of the room exactly.

Answer

To find the longest rod that can measure the three dimensions of the room exactly, we need to determine the highest common factor (HCF) of the three dimensions given.

### Step-by-Step Solution:

1. **Convert all dimensions to the same unit**:
- Length: 6 m 25 cm = 6 * 100 cm + 25 cm = 625 cm
- Breadth: 8 m 75 cm = 8 * 100 cm + 75 cm = 875 cm
- Height: 5 m 50 cm = 5 * 100 cm + 50 cm = 550 cm

2. **List the dimensions**:
- Length = 625 cm
- Breadth = 875 cm
- Height = 550 cm

3. **Find the HCF of the first two dimensions (625 cm and 550 cm)**:
- Use the division method:
- 625 ÷ 550 = 1 (remainder 75)
- Now, take 550 and divide it by the remainder 75:
- 550 ÷ 75 = 7 (remainder 25)
- Now, take 75 and divide it by the remainder 25:
- 75 ÷ 25 = 3 (remainder 0)
- Since the remainder is now 0, the HCF of 625 and 550 is 25 cm.

4. **Now find the HCF of the result (25 cm) with the third dimension (875 cm)**:
- 875 ÷ 25 = 35 (remainder 0)
- Since the remainder is 0, the HCF of 25 cm and 875 cm is also 25 cm.

5. **Conclusion**:
- The longest rod that can measure the three dimensions of the room exactly is **25 cm**.