Question

Length and breadth of a floor is 30 m and 25 m respectively. Find the length of such a longest rope whi
can measure the length and breadth of room completely.
​

Answer 1

Given :

• Length of the floor = 30 m.

• Breadth of the floor = 25 m.

To find :

• The minimum length of the rope that is required to measure the dimensions of the room =?

Step-by-step explanation :

It is Given that,

Length of the floor = 30 m.

Breadth of the floor = 25 m.

Now,

We have to find the length of such a longest rope which measure the length and breadth of room completely. So, we have to find the HCF (Highest Common Factor) of both numbers.

So,

Prime factors of 30 & 25 :-

2 | 30

__|____

3 | 15

__|____

5 | 5

__|____

| 1

5 | 25

__|____

5 | 5

__|____

| 1

So,

→ 30 = 2 × 3 × 5

→ 25 = 5 × 5

•°• HCF = 5

Therefore, the Longest length of the rope that is required to measure the dimensions of the room would be 5 m.