Question

The length, breadth and height of a room are 8m 25cm, 6m 75cm and 4m 50cm respectively. Find the longest tape that can measure the three dimensions of the room exactly.

Answer 1

Answer:

Step-by-step explanation:

╔══╗╔╗ # ╚╗╔╝║║╔═╦╦╦╔╗ ╔╝╚╗║╚╣║║║║╔╣ ╚══╝╚═╩═╩═╩═YOUR 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.

Hope it helps you.//

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