Question

The lengths of the sides of a triagle are 12, 13, and n. Which of the following must be true.

Answer 1

By the triangle inequality theorem we know that
b - a < c < a+b
where a and b are the given sides; c is the unknown side

In this case,
a = 12
b = 13
c = n

So,
b-a < n < b+a
13-12 < n < 13+12
1 < n < 25

So n is both greater than 1 and also less than 25
Broken up, this means n > 1 and n < 25

So it looks like the only answer is choice A. Choices C and D seem to have typos in them? Something seems off about them.