Question

The length, breadth, and height of a room are $825\mathrm{cm},675\mathrm{cm}\mathrm{and}450\mathrm{cm}$ respectively. The longest tape which can measure the three dimensions of the room exactly.

Answer 1

Find the length of the longest tape.

To find the length of the longest tape which can measure the three dimensions of the room, we need to find the H.C.F of length, breadth, and height of the room respectively.

We have to factorize all three given dimensions.

$$\begin{gathered} 825=3\times 5\times 5\times 11 \\ 675=3\times 3\times 3\times 5\times 5 \\ 450=2\times 3\times 3\times 5\times 5 \end{gathered}$$

Thus, $3,5,\mathrm{and}5$ are the common prime factors here.

So, $\mathrm{H}.\mathrm{C}.\mathrm{F}=3\times 5\times 5=75$

Hence, the length of the longest tape should be $75\mathrm{cm}$.