Question

The lengths of two sides of a triangle are $11cm$ and $19cm$. Identify the range of possible lengths for the third side.

• A. $12\mathrm{cm}<\mathrm{x}<30\mathrm{cm}$
• B. $8\mathrm{cm}<\mathrm{x}<30\mathrm{cm}$
• C. $8\mathrm{cm}<\mathrm{x}<31\mathrm{cm}$
• D. $11\mathrm{cm}<\mathrm{x}<19\mathrm{cm}$

Answer 1

The correct option is B

$8\mathrm{cm}<\mathrm{x}<30\mathrm{cm}$

Explanation for the correct option

Finding the range of possible length of the third side.

Given that two sides are $11cm$ and $19cm$

Using triangle law, we can say

The sum of the two sides must be greater than the third side and their difference must be smaller than the third side.

Let the third side be $\mathrm{x}$.

Therefore, the length of the third side can be written as,

$\Rightarrow \mathrm{x}>$Sum of the other two sides and $\mathrm{x}<$Difference between the other two sides

$\Rightarrow$Difference between the other two sides $>\mathrm{x}>$Sum of the other two sides

$$\begin{gathered} \therefore 19-11<\mathrm{x}<19+11 \\ \Rightarrow 8\mathrm{cm}<\mathrm{x}<30\mathrm{cm} \end{gathered}$$

Hence, Option(B) is correct.