Question

1. The length of a floor is 3 m 30 cm and the
breadth is 4 m 44 cm. What is the maximum
length of square tiles that can completely
cover the floor​

Answer 1

Answer:

Step-by-step explanation:

Length of floor = 4 m 44 cm = [ (4 * 100) + 44 ] cm = 444 cm

Breadth of floor = 3 m 30 cm = [ (3 * 100) + 30 ] cm = 330 cm

GCD(Greatest Common Divisor) means to take out the highest common divisor of two positive integers.

Now, we will take Greatest Common Divisor of both numbers,

444 = 2 * 2 * 3 * 37

330 = 2 * 3 * 5 * 11

GCD of 444 and 330 = 2 * 3 = 6

We took those factors which were common in both and multiplied.

Maximum Length of the square tile =>

Greatest number which divides both length and breadth of floor i.e. GCD of 444 and 330

Maximum Length of the square tile => 6 cm

The maximum length of square tiles that can  completely cover the floor is 6 cm.

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