Question

Two sides of a triangle have lengths 5 and 18. Which inequalities represent the possible lengths for the third side, x?

a) 9
b) 5
c) 14
d) none

Answer 1

The possible lengths for the third side, x, of a triangle can be found using the triangle inequality theorem. The correct answer is (c) 14.

Step-by-step explanation:

The possible lengths for the third side, x, of a triangle can be found using the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, the two given sides have lengths 5 and 18, so the possible lengths for the third side, x, are:

x > 18 - 5 = 13

5 + x > 18

Therefore, the correct answer is (c) 14, as 14 satisfies both inequalities.