Question

The length ,breath and height of a room are 8m25cm ,6m75cm and 4m50cm respectively .Find the length of the longest rod that can measure the 3 dimensions of the room exactly.

Answer 1

The dimensions are 825 cm, 675 cm and 450 cm.
For any rod to be capable of measuring a side, the length of the side must be a multiple of the length of the rod.
Hence, we need a rod of length (in cm) which is a factor of 825 , 675 and 450.
For the rod to be of highest possible length we need to find the HCF of 825 , 675 and 450.
Using prime factorization:
825 = 3×52×11

675 = 33×52

450 = 2×32×52

From the above, HCF = 3×52 = 75

Hence, the longest rod which can measure the three dimensions of the room exactly will be 75 cm long.