Question

$p,b,c$ are the side lengths of a triangle $ABC$ with $b=4$ units and $c=8$ units, then

• A. $4<p<12$
• B. $3<p<15$
• C. $4<p<15$

Answer 1

The correct option is A $4<p<12$

For the given triangle $ABC,c=8\&b=4$ units.
Now, according to triangle inequality, sum of the lengths of any two sides is always greater than the length of the third side.
Now, there are three cases:
Case 1: $b+p>c$
$\Rightarrow 4+p>8$
$\Rightarrow p>4$

Case 2: $p+c>b$
$\Rightarrow p+8>4$
Which is true always, so we will ignore this case.

Case 3: $b+c>p$
$\Rightarrow 12>p$

Now, combining all three cases, that are:
$p>4$ and $12>p$
$\therefore$ Combining both the cases, we get:
$4<p<12$