Question

Which of the following correctly indicates whether a triangle can have sides with lengths $3.5,5.3$ and $16.5$, and also provides the correct explanation?

• A. No; $3.5+16.5$ is greater than $5.3$
• B. Yes; $3.5+5.3$ is greater than $16.5$
• C. No; $3.5+5.3$ is less than $16.5$
• D. Yes; $16.5+5.3$ is greater than $3.5$

Answer 1

The correct option is C

No; $3.5+5.3$ is less than $16.5$

Explanation for correct option:

Option(C):
According to triangle inequality theorem that the sum of any two sides of a triangle is greater than third side.
$$\begin{gathered} \Rightarrow 5.3+16.5>3.5 \\ \Rightarrow 3.5+16.5>5.3 \\ \Rightarrow 5.3+3.5<16.5 \end{gathered}$$
Therefore the triangle is not possible

Therefore option(C) is incorrect.

Explanation for incorrect options:

Option(A):
$\Rightarrow 3.5+16.5>5.3$, but the reason is $3.5+5.3=8.8<16.5$
Therefore option(A) is incorrect.
Option(B):
$\Rightarrow 3.5+5.3>16.5$, which is not possible
Therefore option(B) is incorrect.
Option(D):
$\Rightarrow 16.5+5.3>3.5$, but $3.5+5.3=8.8<16.5$
Therefore option(D) is incorrect.

Hence, the correct option is option(C).