Question

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

Answer 1

C)4 < x < 10

Step-by-step 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.