A triangle has side lengths 3 cm, 4 cm, and 5 cm. Is it a right triangle?

• A. No
• B. Sometimes
• C. Not a triangle
• D. Yes

Answer: (D)

A triangle is right-angled when the squares of the two shorter sides add up to the square of the longest side (the Pythagorean theorem). Here, the two shorter sides are 3 cm and 4 cm, and the longest side is 5 cm. Compute: 3^2 + 4^2 = 9 + 16 = 25, which equals 5^2. Since the sum of the squares of the legs matches the square of the longest side, the angle between the 3 cm and 4 cm sides is a right angle. So this triangle is a right triangle. (Also, the numbers 3, 4, and 5 form a famous right-triangle triple, and the triangle inequality is satisfied, so it is indeed a triangle.)