Question

the Length breadth and height of a room are 825 CM 675 cm and 450 CM respectively find the longest tape which can measure the three dimensions of the room exactly​

Answer 1

Given,

Length = 825cm

Breadth = 675cm

Height = 450cm

We should find the HCF of 825,675 and 450 to find the longest tape.

Prime Factorisation of 450 =

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

Prime Factorisation of 675 =

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

Prime Factorisation of 875 =

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

Thus,

450 = 2 × 3 × 3 × 3 × 5 × 5

675 = 3 × 3 × 3 × 5 × 5

875 = 3 × 5 × 5 × 11

Above, 3, 5 and 5 are common factors.

Hence, 3 × 5 × 5 = 75

Therefore, the measure of longest tape is 75cm.