Question

If two sides of the triangle are given as 6 cm and 16 cm, the inequality representing the range of length of third side $x$ (in cm) is:

• A. $x>22$
• B. $x<10$
• C. $10<x<22$
• D. $6<x<16$

Answer 1

The correct option is C $10<x<22$

Given, two sides of the triangle are 6 cm and 16 cm and the length of the third side is $x$ cm.

According to the triangle inequality theorem, the sum of two sides of a triangle is greater than the length of the third side
$\Rightarrow 6+16>x\Rightarrow 22>x\Rightarrow x<22\dots \left(i\right)$

Also, the difference between the two sides is always smaller than the third side.
$\Rightarrow 16-6<x\Rightarrow 10<x\dots \left(ii\right)$

From $\left(i\right)$ and $\left(ii\right),$ we get
$\Rightarrow 10<x<22$

∴ The length of the third side $x$ will be between 10 and 22 cm.