Question

The length, breadth and height of a room are 8m 25cm, 6m 75cm and 4m

50cm, respectively. Determine the longest rod which can measure the three

dimensions of the room exactly.​

Answer 1

Answer:

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.

Answer 2

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