IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .
DIFFERENCE between A and B < length of third side < SUM of A and B

Since the two known sides have lengths 7 and 12, we can write: 12 - 7 < length of third side < 12 + 7

Simplify to get: 5 < length of third side < 19

IF the length of the third side were 5, then the perimeter would equal 7 + 12 + 5 = 24
However, since the length of the third side must be greater than 5, the perimeter must be greater than 24

Likewise, IF the length of the third side were 19, then the perimeter would equal 7 + 12 + 19 = 38
However, since the length of the third side must be less than 5, the perimeter must be less than 38

When we combine both pieces of information we get: 24 < perimeter < 38

The answer choices that work with us in equality are C, D, E and F

Answer: C, D, E, F