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The length, breadth and height of a room are 8 m 25 cm, 6 m 75 cm and 4 m 50 cm, respectively. Determine the longest rod which can measure the three dimensions of the room exactly.
Given: Length, breadth and height of a room are 8 m 25 cm, 6 m 75 cm and 4 m 50 cm respectively.
To find: Here we have to find the length of the longest rod which can measure the three dimensions of the room exactly.
Solution:
First, let's convert all the dimensions in centimetre. So,
Length of the room $=$ 8 m 25 cm $=$ 825 cm
Breadth of the room $=$ 6 m 75 cm $=$ 675 cm
Height of the room $=$ 4 m 50 cm $=$ 450 cm
To find the longest rod which can measure the three dimensions of the room exactly we need to calculate HCF of 825, 675 and 450.
First, let's find HCF of 825 and 675 using Euclid's division algorithm:
Using Euclid’s lemma to get:
- $825\ =\ 675\ \times\ 1\ +\ 150$
Now, consider the divisor 675 and the remainder 150, and apply the division lemma to get:
- $675\ =\ 150\ \times\ 4\ +\ 75$
Now, consider the divisor 150 and the remainder 75, and apply the division lemma to get:
- $150\ =\ 75\ \times\ 2\ +\ 0$
The remainder has become zero, and we cannot proceed any further.
Therefore the HCF of 825 and 675 is the divisor at this stage, i.e., 75.
Now, let's find HCF of 75 and 450 using Euclid's division algorithm:
Using Euclid’s lemma to get:
- $450\ =\ 75\ \times\ 6\ +\ 0$
The remainder has become zero, and we cannot proceed any further.
Therefore the HCF of 75 and 450 is the divisor at this stage, i.e., 75.
So, the length of the longest rod which can measure the three dimensions of the room exactly is 75 cm or 0.75m.
Updated on: 10-Oct-2022
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