#### 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.

#### Solution

Length of room = 8m 25cm = 825 cm

Breadth of room = 6m 75m = 675 cm

Height of room = 4m 50m = 450 cm

∴ The required longest rod

= HCF of 825, 675 and 450

First consider 675 and 450

By applying Euclid’s division lemma

675 = 450 × 1 + 225

450 = 225 × 2 + 0

∴ HCF of 675 and 450 = 825

Now consider 625 and 825

By applying Euclid’s division lemma

825 = 225 × 3 + 150

225 = 150 × 1 + 75

150 = 75 × 2 + 0

HCF of 825, 675 and 450 = 75

Is there an error in this question or solution?

Solution 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. Concept: Euclid’s Division Lemma.