The length, breadth and height of a room are 825 cm, 675 cm and 450 cm respectively. Find the longest tape which can measure the three dimensions of the room exactly.

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Detailed Solution

Here we are given that the length of a room is 825 cm

The breadth of a room is 675 cm

The height of a room is 450 cm

Using the prime factorization method, we will find prime factors of 825, 675, and 450.

825 = 3 × 5 × 5 × 11

675 = 3 × 3 × 3 × 5 × 5

450 = 2 × 3 × 3 × 5 × 5

HCF = 3 × 5 × 5 = 75 cm

The longest tape, which can measure the room's three dimensions, is 75 cm long.

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