The length, breadth and height of a room are 9m75cm, 8m25cm and 6m respectively. Determine the longest tape which can measure the three dimension of the room exactly.
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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
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