Apply the Triangle Inequality Theorem and determine which option could be the third side of the triangle if the two sides measure 4 and 6?

Question

A) 1
B) 9
C) 11
D) 2
only pick one number not any other stuff

Answer 1

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side.

In this case, the two sides measure 4 and 6. To determine which option could be the third side, we need to check if the sum of the two given sides is greater than the option.

Option A) 4 + 6 > 1
10 > 1

Option B) 4 + 6 > 9
10 > 9

Option C) 4 + 6 > 11
10 > 11 (not true)

Option D) 4 + 6 > 2
10 > 2

Based on the Triangle Inequality Theorem, the sum of the lengths of the two sides of the triangle is always greater than the length of the third side. Therefore, the third side could be Option A) 1.