By the triangle inequality theorem, if two sides of a triangle have lengths of 3 and 7, what are all the possible lengths of the third side? a) 3 < x < 8 b) 3 < x < 7 c) 4 < x < 10 d) 5 < x < 7

C)4 < x < 10

Explanation:

Using the triangle inequality theorem, adding the other 2 sides would give you a value greater than the missing side (3 + 7= 10, so x < 10), and subtracting them would give you a value less than the missing side (7 - 3 = 4, so x > 4). Combine the equations and get 4 < x < 10.