Question

A room is 5m60cm long and 2m40cm broad. What is the dimension of the
largest square tile that can be fixed on the floor so that the tile need not be
cut to fit the floor?

Answer 1

Answer:

The answer is that the largest square tile that can be fixed on the floor is a square tile with a side length of 80 cm.

Step-by-step explanation:

To find the dimension of the largest square tile that can be fixed on the floor without cutting, we need to find the greatest common divisor (GCD) of the length and breadth of the room. Once we have the GCD, we can use it as the side length of the square tile.

Step 1: Convert the measurements to centimeters for easier calculation.

Length of the room = 560 cm

Breadth of the room = 240 cm

Step 2: Find the GCD of the length and breadth.

We can use the Euclidean algorithm to find the GCD. The algorithm works as follows:

Divide the larger number by the smaller number.

Take the remainder and divide the previous smaller number by it.

Repeat until the remainder is zero. The last non-zero remainder is the GCD.

240 does not divide evenly into 560, so we perform the first division:

560 ÷ 240 = 2 remainder 80

Then we divide 240 by 80:

240 ÷ 80 = 3 remainder 0

Therefore, the GCD of 560 and 240 is 80 cm.

Step 3: Use the GCD as the side length of the square tile.

Since the GCD is 80 cm, we can use this as the side length of the square tile. The largest square tile that can be fixed on the floor without cutting is therefore a tile with side length 80 cm.

So the answer is that the largest square tile that can be fixed on the floor is a square tile with a side length of 80 cm.

To learn more about similar question visit:

https://brainly.in/question/8427431?referrer=searchResults

https://brainly.in/question/4696061?referrer=searchResults

#SPJ1