Final answer:
The legs of a right triangle with a hypotenuse of 15 units could be 9 units and 12 units as this is a set of whole numbers that satisfies the Pythagorean theorem, a² + b² = c².
Step-by-step explanation:
The lengths of the legs of a right triangle with a hypotenuse of length 15 units can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c². When the lengths of the legs are whole numbers, the triangle is often referred to as a Pythagorean triple. For a hypotenuse of length 15, the only set of whole number leg lengths that satisfy the Pythagorean theorem are 9 units and 12 units, since 9² + 12² = 81 + 144 = 225, which is the square of 15.