Question

Consider a degenrate triangle $ABC$, with side lengths as $a,b,c$ such that $a=10\text{cm};b=6\text{cm}$, then the length of the third side $c=$

• A. $5\text{cm}$
• B. $10\text{cm}$
• C. $4\text{cm}$

Answer 1

Answer: (A), (C)

$4\text{cm}$

Given $△ABC$ as a degenerate triangle.
$\Rightarrow$ The length of any two sides is equal to the length of the third side.
Here, $a=10\text{cm},b=6\text{cm}$
Now, if $c$ is the length of the third side:
There are two possible cases:
Case 1: $c=$ Sum of $a$ and $b$
$\Rightarrow c=a+b=16\text{cm}$
Case 2: $b+c=a$
$\Rightarrow c=a-b=4\text{cm}$
$\therefore c$ can be either $16\text{cm}$ or $4\text{cm}$
From the options, $4\text{cm}$ is there, hence we will choose $4\text{cm}$