Question

Name all of the possible values for x in the triangle below. show your work.​

Answer 1

• 3 < x < 17

Explanation:

As per triangle inequality theorem, sum of the lengths of any two sides must be greater than the length of the third side.

• x < 10 + 7 ⇒ x < 17
• 7 < x + 10 ⇒ x > -3
• 10 < x + 7 ⇒ x > 3

Combination of the inequalities above:

• 3 < x < 17

The value of x must be between 3 and 17 units