Question

Two sides of a triangle are 8 and 11 units Which of the following length can be the length of the third side?

• A. 12 cm
• B. 2 cm
• C. 24 cm
• D. None of these

Answer 1

The correct option is A 12 cm

We know the basic rule related to the sides of a triangle-

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

Let the third side be $x$.

We can form an equation-

$\Rightarrow$ $8+11>x$

$\Rightarrow$ $19>x$ ------ ( 1 )

That means the possible values of $x$ are less than $19.$

We can form another equation -

$\Rightarrow$ $8+x>11$

$\Rightarrow$ $x>11-8$

$\Rightarrow$ $x>3$ ------ ( 2 )

That means the possible values of $x$ are greater than $3.$

On combining equation ( 1 ) and ( 2 )-

$\Rightarrow$ $3<x<19$

Option A is correct.