Final answer:
To determine if the sets of sides can form a right triangle, we apply the Pythagorean theorem. The sets √27, √35, 6 and √12, 3, √21 satisfy the theorem and therefore can form right triangles.
Step-by-step explanation:
To determine which set of side measurements could be used to form a right triangle, we must apply the Pythagorean theorem.
According to this theorem, for any right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). This relationship is expressed as a² + b² = c².
To figure out if the given sets of sides can form a right triangle, we must check this equation for each set. Let's evaluate each of the following:
- For the set 6, 12, 60, we get 6² + 12² = 36 + 144, which is not equal to 60² (3600), so this set cannot form a right triangle.
- For the set √27, √35, 6, we find (√27)² + (√35)² = 27 + 35, which gives us 62 = 6². So, √27, √35, and 6 can indeed form a right triangle.
- For the set √12, 3, √21, we have (√12)² + 3² = 12 + 9, which equals 21. This equals (√21)², so √12, 3, and √21 can form a right triangle as well.
Therefore, the sets √27, √35, 6 and √12, 3, √21 can both be used to form a right triangle.