Final answer:
Using the Pythagorean theorem, it is determined that only the set of sides in option d (15, 20, 25) forms a right triangle as their lengths satisfy the equation a² + b² = c².
Step-by-step explanation:
To determine which set of sides can form a right triangle, we will use the Pythagorean theorem, which states that for a right triangle with legs 'a' and 'b', and hypotenuse 'c', the relationship is a² + b² = c².
- For set a (9, 13, 15), we check if 9² + 13² = 15². Calculating this gives us 81 + 169 = 250, which is not equal to 225 (15²), so set a cannot be the sides of a right triangle.
- For set b (2, 4, 5), we check if 2² + 4² = 5². Calculating gives 4 + 16 = 20, which is not equal to 25 (5²), so set b also cannot be the sides of a right triangle.
- For set c (3, 5, 9), we check if 3² + 5² = 9². Calculating gives 9 + 25 = 34, which is not equal to 81 (9²), so set c cannot be the sides of a right triangle either.
- Finally, for set d (15, 20, 25), we check if 15² + 20² = 25². Calculating this gives 225 + 400 = 625, which is equal to 625 (25²), so set d can indeed be the sides of a right triangle.
Hence, only the set of sides in option d (15, 20, 25) can be the sides of a right triangle.
Additionally, it's true that we can use the Pythagorean theorem to calculate various things, such as the straight-line distance between two points, or the length of the resultant vector obtained from the addition of two vectors which are at right angles to each other, as in question 36.