Question

The length , breadth and height of a hall is 3675cm ,2100cm , 1050cm respectively . What can be the maximum length of a tape by which we can measure the length, breadth and height of the hall​?

Answer 1

The maximum length of a tape that can measure the length, breadth, and height of the hall is 525 cm, which is the greatest common divisor of the three given dimensions.

Step-by-step explanation:

To find the maximum length of a tape that can measure the length, breadth, and height of the hall without changing the tape's position, we need to calculate the greatest common divisor (GCD) of the three dimensions. The dimensions given are 3675 cm, 2100 cm, and 1050 cm. We can find the GCD of these three numbers using the Euclidean algorithm or any other method of finding GCDs.

First, find the GCD of two of the numbers, say 3675 and 2100:

1. 3675 ÷ 2100 gives a remainder of 1575.
2. 2100 ÷ 1575 gives a remainder of 525.
3. 1575 ÷ 525 gives a remainder of 0, which means 525 is a common divisor of both 3675 and 2100.

Next, find the GCD of this result (525) with the third number (1050):

1. 1050 ÷ 525 also gives a remainder of 0, meaning 525 is a common divisor of all three numbers.

Therefore, the maximum length of a tape that can measure the three dimensions of the hall is 525 cm.