Question

The longest tape which can be used to measure exactly the lengths $175cm$,$450cm$ and $650cm$ is

• A. $25cm$
• B. $50cm$
• C. $75cm$
• D. $125cm$

Answer 1

The correct option is A

$25cm$

Explanation:

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 room respectively.

Length of the room $=175$ $cm$

Breadth of the room $=450cm$

Height of the room$=650cm$

Let us factorize all three given dimensions.

$$\begin{gathered} 175=\overline{)5}\times \overline{)5}\times 7 \\ 450=2\times 3\times 3\times \overline{)5}\times \overline{)5} \\ 650=2\times \overline{)5}\times \overline{)5}\times 13 \end{gathered}$$

Here, $5$ and $5$ are the common prime factors.

H.C.F$\left(175,450,650\right)=5\times 5$

H.C.F$\left(175,450,650\right)=25$

we need $25cm$ the longest tape to measure the three dimensions of the room.

Therefore,option-$\mathrm{A}$ is the correct answer.