Question

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.

Answer 1

From the question, it’s given that 

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 

The required longest rod which can measure the room exactly is the HCF of 825, 675 and 450. 

First, consider 675 and 450 and apply Euclid’s division lemma, 

675 = 450 x 1 + 225 

450 = 225 x 2 + 0 

Therefore, the HCF (675, 450) = 225 

Now, consider 225 and the third dimension i.e., 825 

By applying Euclid’s division lemma to the above, 

825 = 225 x 3 + 150 

225 = 150 x 1+75 

150 = 75 x 2 + 0 (here the remainder becomes 0) 

Thus, HCF (225, 825) = 75. 

Therefore, HCF of 825, 675 and 450 is 75. 

And, the length of the longest rod is 75 cm or 0.75 m.