Question

Which statement is true about the difference of any two sides of a triangle?

• A. It is greater than the third side
• B. It is zero
• C. It is lesser than the third side
• D. It is lesser than zero

Answer 1

The correct option is C It is lesser than the third side

Let $a,b,c$ be the sides of triangle.

For constructing a triangle sum of any two sides must be greater than third side

$\Rightarrow a+b>c$

$\Rightarrow a>c-b$

$\Rightarrow c-b<a.......\left(i\right)$

Also $a+c>b$

$\Rightarrow c>a-b$

$\Rightarrow a-b>c.....\left(ii\right)$

Also $b+c>a$

$\Rightarrow c>a-b$

$\Rightarrow a-b>c.......\left(iii\right)$

From $\left(i\right),\left(ii\right)$ and $\left(iii\right)$ it is clear that difference of any two sides is greater than the third side.

So option $C$ is correct.