Final answer:
The length of the hypotenuse in a right triangle can be determined using the Pythagorean Theorem, which confirms that the hypotenuse of a triangle with legs 5 and 12 is indeed 13.
Step-by-step explanation:
Understanding the Hypotenuse in a Right Triangle
The length of the hypotenuse in a right triangle can be determined using the Pythagorean Theorem, which states that a² + b² = c². In this context, 'a' and 'b' represent the lengths of the legs of the triangle, and 'c' represents the length of the hypotenuse. Specifically, when the lengths of the legs are 5 and 12, we calculate the hypotenuse by squaring both legs and adding the results: 5² + 12² = 25 + 144 = 169. Taking the square root of 169 yields 13, confirming that the length of the hypotenuse is indeed 13.
According to the given options, the correct answer is (a) The Pythagorean Theorem confirms it. This is because the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse. Neither the angle sum nor the area of the triangle plays a role in confirming the length of the hypotenuse for a right triangle.