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

a. N>1

b. N<13

c. 1 d. 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.