The triple (3, 4, 5) demonstrates what in a right triangle?

The triple (3, 4, 5) demonstrates what in a right triangle?

• A. An isosceles triangle
• B. A scalene triangle
• C. A median
• D. A Pythagorean triple (right triangle)

Answer: (D)

This shows a Pythagorean triple, which are sets of three integers that can be the side lengths of a right triangle with the two shorter sides as legs and the longest side as the hypotenuse. Here, 3^2 + 4^2 = 9 + 16 = 25, and 5^2 = 25, so the relationship a^2 + b^2 = c^2 holds with integers 3, 4, and 5. That makes it a Pythagorean triple. The triangle is also scalene (all sides are different), but the term that specifically describes this right-triangle side-length relationship is a Pythagorean triple. It isn’t about a median, which is a line segment inside the triangle, not about the side lengths.

This shows a Pythagorean triple, which are sets of three integers that can be the side lengths of a right triangle with the two shorter sides as legs and the longest side as the hypotenuse. Here, 3^2 + 4^2 = 9 + 16 = 25, and 5^2 = 25, so the relationship a^2 + b^2 = c^2 holds with integers 3, 4, and 5. That makes it a Pythagorean triple.

The triangle is also scalene (all sides are different), but the term that specifically describes this right-triangle side-length relationship is a Pythagorean triple. It isn’t about a median, which is a line segment inside the triangle, not about the side lengths.