Question

Two sides of a triangle measure 25 and 38. Circle all possible side lengths of the third side from the numbers listed below:

13, 13, 14, 17, 19.4, 46, 63, 71

Answer 1

Let x be the third side of this triangle. We can't find a single value for x because x can range between a boundary of values. The interval for x is

38-25 < x < 38 + 25
13 < x < 63

So as long as x is between 13 and 63 (ignore the endpoints themselves), then we have a valid possible third side length. The values that fit this description are...

14, 17, 19.4, 46

which are the answers

the other values (13, 63, 71) are outside of the interval mentioned