Question

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

Answer 1

Solution:
Since, 1m = 100 cm
Therefore, 8 m 25 cm = 825 cm
6 m 75 cm = 675 cm
4 m 50 cm = 450 cm
HCF(825, 675, 450) will give the length of the longest rod.
825 = 675 x 1 + 150
675 = 150 x 4 + 75
150 = 75 x 2 + 0
Therefore, HCF(825, 675) = 75
450 = 75 x 6 + 0
=> HCF(450, 75) = 75
=> HCF (825, 675, 450) = 75
Hence, the length of the longest rod is 75 cm.