Question

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

Valid answers only irrelevant answers will be reported​

Answer 1

Answer:

For the rod to be of highest possible length we need to find the HCF of 825 , 675 and 450. Hence, the longest rod which can measure the three dimensions of the room exactly will be 75 cm long.

Answer 2

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.