In each case, determine if the sides form a right triangle. If they do, place in the Yes column. If they do not, place in the No column.

Question

Put responses in the correct input to answer the question.
Yes No

1. 9,12,14
2. 6,9,12
3. 5,12,13
4. 3,4,5

Answer 1

To determine if the sides form a right triangle, we can use the Pythagorean theorem, which states that for a triangle with sides a, b, and c (where c is the longest side), the relationship a² + b² = c² must hold true.

Let's analyze each set of sides:

1. 9, 12, 14:
   \( 9^2 + 12^2 = 81 + 144 = 225 \)
   \( 14^2 = 196 \)
   Does not satisfy the condition.
   No

2. 6, 9, 12:
   \( 6^2 + 9^2 = 36 + 81 = 117 \)
   \( 12^2 = 144 \)
   Does not satisfy the condition.
   No

3. 5, 12, 13:
   \( 5^2 + 12^2 = 25 + 144 = 169 \)
   \( 13^2 = 169 \)
   Satisfies the condition.
   Yes

4. 3, 4, 5:
   \( 3^2 + 4^2 = 9 + 16 = 25 \)
   \( 5^2 = 25 \)
   Satisfies the condition.
   Yes

Now, let's put this in the proper format:

Yes
3. 5,12,13
4. 3,4,5

No

1. 9,12,14
2. 6,9,12