A triangle has side lengths of 20 cm, 99 cm, and 108 cm. classify it as acute, obtuse, or right?

Solution:

The side lengths of a triangle is 20 cm, 99 cm, and 108 cm (Given)

• An obtuse triangle has an angle greater than 90° and lesser than 180° in its interior.
• One angle is obtuse and the other two angles are acute in an obtuse triangle.

We can analyze it by drawing an image of the given measurement.

We know that for an obtuse triangle, the square of the third side > the sum of the squares of the other two sides.

108² = 11664

99² + 20² = 9801+ 400 =10201

108² > 99² + 20²

Therefore, the triangle is obtuse.  

A triangle has side lengths of 20 cm, 99 cm, and 108 cm. Classify it as acute, obtuse, or right?

Summary:

A triangle that has side lengths of 20 cm, 99 cm, and 108 cm is obtuse.