Question

The length, breadth and height of a room are 8m 50cm, 6m 25cm and 4m 75cm respectively. Find the length of the longest rod that can measure the dimensions of the room exactly.

Answer 1

Given,

Length, L = 8 m 50 cm = 850 cm $=2^1\times 5^2\times 17$

Breadth, B = 6m 25cm = 625 cm $5^4$

Height, H = 4m 75cm = 475 cm $=5^2\times 19$

The longest rod that can measure the dimensions of the room exactly, will be equal to the HCF of length,breadth and height of the room.

$\therefore$ HCF of L, B and H is $5^2$ = 25cm

$\therefore$ Length of the longest rod = 25 cm