question_answer

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

Answer:

To find the length of the longest rod that can measure the dimensions of the room exactly, we have to find HCF.

Length, \[L=8\text{ }m\text{ }50\text{ }cm=850\text{ }cm={{2}^{1}}\times {{5}^{2}}\times 17\]

Breadth, \[B=6\text{ }m\text{ }25\text{ }cm=625\text{ }cm={{5}^{4}}\]

Height, \[H=4\text{ }m\text{ }75\text{ }cm=475\text{ }cm={{5}^{2}}\times 19\]

\[\therefore \] HCF of L, B and His \[{{5}^{2}}=25\text{ }cm\]

\[\therefore \] Length of the longest rod \[=25\text{ }cm\]