Question

Is anyone good with triangle inequalities? I provided a picture for the problem.

Answer 1

1 < x < 19

Explanation:

Triangle Inequality Theorem

Let y and z be two of the side lengths of a triangle. The length of the third side x cannot be any number. It must satisfy all the following restrictions:

x + y > z

x + z > y

y + z > x

Combining the above inequalities, and provided y>z, the third size must satisfy:

y - z < x < y + z

We are given the measures y=10, z=9. The third side must satisfy:

10 - 9 < x < 10 + 9

1 < x < 19