Question

If the lengths of two sides of a triangle are $6cm$ and $10cm$, then the length of the third side can be:

• A. $3cm$
• B. $4cm$
• C. $2cm$
• D. $6cm$

Answer 1

The correct option is D

$6cm$

Explanation for the correct option:

Calculate the possible length of the third side:

It is given that the lengths of two sides of a triangle are $6cm$ and $10cm$.

Let, the length of the third side be $acm$.

Now, according to the triangle inequality

The sum of lengths of any two sides of a triangle is always greater than the length of the third side.

So, first side $+$ second side $>$ third side

$\Rightarrow$ $10+6>a$

$\Rightarrow$ $16>a$ $...\left(\mathrm{i}\right)$

Again, according to the triangle inequality,

The difference in lengths of any two sides of a triangle is always smaller than the length of the third side.

So, first side $-$ second side $<$ third side

$\Rightarrow$ $10-6<a$

$\Rightarrow$ $4<a$ $...\left(\mathrm{i}\right)$

From the inequalities $\left(\mathrm{i}\right)$ and $\left(\mathrm{ii}\right)$, we have,

$4<a<16$

It means that the length of $a$ is greater than $4cm$ and smaller than $16cm$

So, out of the given options, only option (D) i.e. $6cm$ is possible.

Hence, option (D) is the correct answer.