A triangle has sides 5, 5, and 6. What type of triangle is it?

A triangle has sides 5, 5, and 6. What type of triangle is it?

• A. Equilateral
• B. Scalene
• C. Isosceles
• D. Right

Answer: (C)

Having two equal sides makes the triangle isosceles. Here the side lengths are 5, 5, and 6, so the two sides of length 5 are equal and the third side is different. An equilateral triangle would need all three sides equal, which isn’t the case, and a scalene triangle has all sides different, which also isn’t the case. A right triangle would meet the Pythagorean condition with the largest side as the hypotenuse: 5^2 + 5^2 = 25 + 25 = 50, which does not equal 6^2 = 36, so it’s not right. Since two sides are equal, the triangle is isosceles, and the angles opposite those equal sides are equal.

Having two equal sides makes the triangle isosceles. Here the side lengths are 5, 5, and 6, so the two sides of length 5 are equal and the third side is different. An equilateral triangle would need all three sides equal, which isn’t the case, and a scalene triangle has all sides different, which also isn’t the case. A right triangle would meet the Pythagorean condition with the largest side as the hypotenuse: 5^2 + 5^2 = 25 + 25 = 50, which does not equal 6^2 = 36, so it’s not right. Since two sides are equal, the triangle is isosceles, and the angles opposite those equal sides are equal.