Question

The measures of two sides of a triangle are 4in and 13in. Find all possible values that the third side of this triangle can be?

Answer 1

9 < x < 17 is the possible length of the third side of a triangle.

Explanation:

The Triangle Inequality theorem defines that if we are given two sides of a triangle, the sum of any two given sides of a triangle must be greater than the measure of the 3rd side.

Given the two sides of the triangle

• 4 in

• 13 in

Let 'x' be the length of 3rd size.

According to the Triangle Inequality theorem,

The difference of two sides < x < The sum of two sides

13 - 4 < x < 13+4

9 < x < 17

Therefore, 9 < x < 17 is the possible length of the third side of a triangle.