Final answer:
The question involves using the Pythagorean theorem to confirm that the lengths of the legs and hypotenuse of the provided options form valid right triangles.
Step-by-step explanation:
The question deals with the application of the Pythagorean theorem which is a fundamental concept in mathematics, specifically geometry. This theorem states that in a right-angled triangle the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides, or mathematically expressed as a² + b² = c².
To find the lengths of the legs and hypotenuse of a right triangle, you can use the given lengths of the legs (a and b) and calculate the length of the hypotenuse (c) using the formula c = √(a² + b²). For example, if the legs of the triangle are 3 units and 4 units long, you can calculate the hypotenuse as follows: c = √(3² + 4²) = √(9 + 16) = √25 = 5. This confirms that the hypotenuse is 5 units long when the legs are 3 units and 4 units respectively, matching with one of the options provided by the student.