Classify the triangle with sides 5, 12, and 13.

• A. Acute triangle
• B. Right triangle
• C. Obtuse triangle
• D. Equilateral triangle

Answer: (B)

A triangle is right-angled when the squares of two sides add up to the square of the third side. Here, 5^2 + 12^2 = 25 + 144 = 169, which equals 13^2. That means the angle between the sides of lengths 5 and 12 is 90 degrees, so the triangle is a right triangle. The 13 side is the hypotenuse. This 5-12-13 set is a classic Pythagorean triple. It isn’t acute because there’s a 90-degree angle, and it isn’t obtuse or equilateral for the same reason (not all angles < 90, no angle > 90, and the sides aren’t all equal).