# 8.5.4. Triangle Inequality

Determine the perimeter of the triangle that has one axis of symmetry, given that the lengths of two of its sides are cm and cm.

• Acm
• Bcm
• Ccm
• Dcm

### Example

Determine the perimeter of the triangle that has one axis of symmetry, given that the lengths of two of its sides are cm and cm.

### Solution

Step 1: Determine the length of the third side.

A triangle with one axis of symmetry must be an isosceles triangle.

An isosceles triangle has two side lengths that are equal in length. So, the third side length of this triangle must be either or .

The triangle inequality states that the sum of the lengths of any two sides of a triangle is greater than the length of the other side.

Check the sum of side lengths to see if the third side can be .

The sum of and is not greater than , so the third side cannot be .

Then check the sum of side lengths to see if the third side can be .

Therefore, the third side length side is .

Step 2: Find the perimeter.

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