Question

the Length breadth and height of a room are 825cm, 675cm, and 450cm find the longest dimensions of the room exactly​.

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Answer 1

Solution:

Given:

=> Length of room = 825 cm

=> Breadth of room = 675 cm

=> Height of the room = 450 cm

To find:

=> Longest tape to measure dimensions of the room.

Formula used:

=> HCF

Now, we will find the HCF of all the dimensions of the room to calculate that longest tape.

HCF of 825:

$\begin{gathered}\begin{array}{r | l}3 & 825 \\\cline{2-2} 5 & 275 \\\cline{2-2} 5 & 55 \\\cline{2-2} 11 & 11 \\\cline{2-2} & 1\end{array}\end{gathered}$

HCF of 675:

$\begin{gathered}\begin{array}{r | l}3 & 675 \\\cline{2-2} 3 & 225 \\\cline{2-2} 3 & 75 \\\cline{2-2} 5 & 25 \\\cline{2-2} 5 & 5 \\\cline{2-2} & 1\end{array}\end{gathered}$

HCF of 450:

$\begin{gathered}\begin{array}{r | l}2 & 450 \\\cline{2-2} 3 & 225 \\\cline{2-2} 3 & 75 \\\cline{2-2} 5 & 25 \\\cline{2-2} 5 & 5 \\\cline{2-2} & 1\end{array}\end{gathered}$

Therefore,

825 = 3 × 5 × 5 × 11

625 = 3 × 3 × 3 × 5 × 5

450 = 2 × 3 × 3 × 5 × 5

HCF of 825, 675 and 450 = 3 × 5 × 5 = 75 cm

Hence, longest tape = 75 cm.