Question

A triangle has side lengths of 12 cm, 5 cm, and 9 cm. Classify it as acute, obtuse, or right.

Answer 1

We know

Pythagorean theorem states

• H²=P²+B²

If it's true triangle is right .

If

LHS>RHS triangle is obtuse and vice versa

Here

• 5²+9²=106

Which is less than 12²=144

Obtuse triangle

Answer 2

• Obtuse

Explanation:

Use Pythagorean to determine the type of the triangle.

If the square of the longest side is equal to sum of the squares of the other sides, it is right, if smaller, then the triangle is acute, if greater, then the triangle is obtuse.

• 5² + 9² ? 12²
• 25 + 81 ? 144
• 106 < 144

This shows the angle opposite to the longest side is greater than 90°

Hence the triangle is obtuse