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

The length of the longest tape will be the HCF of 825, 675, and 450.

Answer: The longest tape which can measure the three dimensions of the room exactly is 75 cm.

Let's find the length of the longest tape which can measure the three dimensions of the room exactly.

Explanation:

The longest tape which can measure the three dimensions of the room exactly will be the Highest common factor of the length, breadth, and height of the room.

Thus, we will calculate the HCF of 825, 675 and 450

Let's prime factorise the numbers 825, 675 and 450

825 = 3 × 5 × 5 × 11

675 = 3 × 3 × 3 × 5 × 5

450 = 2 × 3 × 3 × 5 × 5

Hence, the HCF(825, 675, 450) = 3 × 5 × 5 = 75

Thus, the longest tape which can measure the three dimensions of the room exactly is 75 cm.