Which of the following lengths could form the sides of a right triangle? 5,13,12 15,6,16 $$ 5,6,11 $$ $$ 5,16,17 $$

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To determine if the given lengths can form the sides of a right triangle, we need to check if they satisfy the Pythagorean theorem. The Pythagorean 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.

Let's check each set of lengths:

1. 5, 13, 12:
   - $$5^2 + 12^2 = 25 + 144 = 169$$
   - $$13^2 = 169$$
   Since $$5^2 + 12^2 = 13^2$$, the lengths 5, 13, and 12 can form the sides of a right triangle.

2. 15, 6, 16:
   - $$15^2 + 6^2 = 225 + 36 = 261$$
   - $$16^2 = 256$$
   Since $$15^2 + 6^2 
eq 16^2$$, the lengths 15, 6, and 16 cannot form the sides of a right triangle.

3. 5, 6, 11:
   - $$5^2 + 6^2 = 25 + 36 = 61$$
   - $$11^2 = 121$$
   Since $$5^2 + 6^2 
eq 11^2$$, the lengths 5, 6, and 11 cannot form the sides of a right triangle.

4. 5, 16, 17:
   - $$5^2 + 16^2 = 25 + 256 = 281$$
   - $$17^2 = 289$$
   Since $$5^2 + 16^2 
eq 17^2$$, the lengths 5, 16, and 17 cannot form the sides of a right triangle.

Therefore, only the lengths 5, 13, and 12 can form the sides of a right triangle.
The lengths 5, 13, and 12 can form the sides of a right triangle.

Which of the following lengths could form the sides of a right triangle? 5,13,12 15,6,16 \( 5,6,11 \) \( 5,16,17 \)

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