# 8.5.3. Comparing the Lengths of Sides of a Triangle

Arrange the lengths of , , , and in ascending order.

• A
• B
• C
• D

### Example

Arrange the lengths of , , , and in ascending order.

### Solution

Step 1: Arrange the side lengths of in ascending order.

First, find . and are supplementary (with a sum of ).

Then, find using the sum of the angle measure in .

So, , , and .

For any triangle, the longest side is opposite to the greatest angle measure, and the shortest side is opposite to the smallest angle measure.

The greatest angle measure in is so is the longest side. We also know this is true because the hypotenuse of a right triangle is always the longest side. The smallest angle measure is , so is the shortest side.

It is given that , so we also know that .

Step 2: Arrange the 4 original lengths in ascending order.

Since , is an obtuse angle and the side opposite to the -angle is longer than either of the other two sides of the obtuse triangle.

So, the 4 lengths arranged in ascending order are: .

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