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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
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B
3<p<15
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C
4<p<15
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Solution

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
4+p>8
p>4

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

Case 3: b+c>p
12>p

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



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