Question

The length of the two sides of a triangle are $7\mathrm{cm}\mathrm{and}9\mathrm{cm}$. The length of the third side may lie between,

• A. $1\mathrm{cm}\mathrm{and}10\mathrm{cm}$
• B. $2\mathrm{cm}\mathrm{and}8\mathrm{cm}$
• C. $3\mathrm{cm}\mathrm{and}16\mathrm{cm}$
• D. $1\mathrm{cm}\mathrm{and}16\mathrm{cm}$

Answer 1

The correct option is C

$3\mathrm{cm}\mathrm{and}16\mathrm{cm}$

The explanation for the correct option.

Let us consider the length of the third side of the triangle is $m$.

As we know that the sum of the two sides of the triangle is greater than the third side.

$$\begin{gathered} \therefore 7+9>m \\ 16>m \end{gathered}$$

Now, the difference between the two sides $=9–7=2\mathrm{cm}$

Thus, the third side is greater than $2\mathrm{cm}$ and smaller than $16\mathrm{cm}$.

Hence, the correct option is $C$.