Longest Rod to Measure the Dimensions of a Room Exactly

Video Explanation

Watch the video below to understand the complete solution step by step:

Solution

Question: The length, breadth and height of a room are 8 m 25 cm, 6 m 75 cm and 4 m 50 cm respectively. Determine the longest rod which can measure the three dimensions of the room exactly.

Step 1: Convert All Dimensions into Centimetres

Length = 8 m 25 cm = 8 × 100 + 25 = 825 cm

Breadth = 6 m 75 cm = 6 × 100 + 75 = 675 cm

Height = 4 m 50 cm = 4 × 100 + 50 = 450 cm

Step 2: Find the HCF of 825, 675 and 450

Using Euclid’s division algorithm:

825 = 675 × 1 + 150

675 = 150 × 4 + 75

150 = 75 × 2 + 0

So, HCF (825, 675) = 75

Now find HCF of 75 and 450:

450 = 75 × 6 + 0

∴ HCF (825, 675, 450) = 75

Final Answer

∴ The longest rod which can measure the three dimensions of the room exactly is 75 cm.

Conclusion

Thus, by converting all measurements into the same unit and applying Euclid’s division algorithm, we find that the required longest rod is 75 cm.