Question

If the lengths of two sides of a triangle are 6 and 7, the length of the third side may be

Answer 1

• The third side may be between 1 and 13 units

Explanation:

Let the missing side is x.

According to the triangle inequality theorem, the sum of any two sides of a triangle is greater than the third side.

We have inequalities:

• 6 + 7 > x ⇒ x < 13
• 6 + x > 7 ⇒ x > 1
• 7 + x > 6 ⇒ x > - 1

The common solution is:

• 1 < x < 13