Question

The sides of ΔDEF are d, e, and f. If the lengths of d = 12 and e = 19, what are the possible lengths of f? ANSWERS: A) 7 < f < 19 B) 7 < f < 31 C) 12 < f < 19 D) 12 < f < 31

Answer 1

b

Explanation:

7 < f < 31

Answer 2

B

Explanation:

There are two cases: Either f is the longest side or f is the shortest side. If we look at the first case, f < 12 + 19 which means f < 31. The second case tells us that 12 + f > 19 which means f > 7 so the answer is 7 < f < 31.