The length, breadth and height of a room are 8 m 25 cm, 6 m 75 cm and 4 m 50 cm, respectively.

We are given the length, breadth and height of a room as 8m 25cm, 6m 75cm and 4m 50cm, respectively. We need to determine the largest room which can measure the three dimensions of the room exactly.

We first convert each dimension in cm

Length of room = 8m 25cm = 825cm

Breadth of room = 6m 75cm = 675cm

Height of room = 4m 50cm = 450cm.

Therefore, the required longest rod = H.C.F. of 825, 675 and 450.

First we consider 675 and 450.

By applying Euclid’s division lemma

$675=450 \times 1+225$

$450=225 \times 2+0$

Therefore, H.C.F. of 675 and 450 = 225

Now, we consider 225 and 825.

By applying Euclid’s division lemma

$825=225 \times 3+150$

$225=150 \times 1+75$

$150=75 \times 2+0$

Therefore, H.C.F. of 825, 675 and 450 = 75

Hence, the length of required longest rod is 75cm