A right triangle has side lengths 13 centimeters, 84 centimeters, and 85 centimeters. What is the length of the side opposite the right angle and why? 85 centimeters, because the longest side is opposite the right angle. 85 centimeters, because it is a multiple of 5 . 84 centimeters, because it is a multiple of 2 . 84 centimeters, because the second-longest side is opposite the right angle.

The length of the side opposite the right angle is 85 centimeters, and here's why: In any right triangle, the side opposite the right angle is called the hypotenuse, which is always the longest side. Therefore, in this triangle, the hypotenuse measures 85 centimeters, and it holds the crucial role of providing the base for calculating the relationship between the other two sides using the Pythagorean theorem. Fun fact! The Pythagorean theorem tells us that in a right triangle, the square of the hypotenuse length equals the sum of the squares of the other two sides. If you calculate it for this triangle: \( 13^2 + 84^2 = 169 + 7056 = 7225 \), and \( 85^2 = 7225 \) as well! This mesmerizing connection is what makes right triangles so uniquely special in math.