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Question
The dimensions of a room are 6m 75cm, 4m 50cm and 2m 25cm. Find the length of the largest measuring rod which can measure the dimensions in exact number of times.
The dimensions of a room are 6m 75cm, 4m 50cm and 2m 25cm. Find the length of the largest measuring rod which can measure the dimensions in exact number of times.
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Solution
The dimensions are 225 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 225 , 675 and 450.
For the rod to be of highest possible length we need to find the HCF of 225 , 675 and 450.
Using prime factorization: 225 = 32×52
675 = 33×52
450 = 2×32×52
From the above, HCF = 32×52 = 225
Hence, the longest rod which can measure the three dimensions of the room exactly will be 225 cm long.
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 225 , 675 and 450.
For the rod to be of highest possible length we need to find the HCF of 225 , 675 and 450.
Using prime factorization:
225 = 32×52
675 = 33×52
450 = 2×32×52
From the above, HCF = 32×52 = 225
Hence, the longest rod which can measure the three dimensions of the room exactly will be 225 cm long.
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