In the Pythagorean triple (9, 12, 15), the side lengths represent a right triangle where:
- \( c \) (the hypotenuse) = 15
- \( a \) and \( b \) are the other two sides, which are 9 and 12.
Since the values \( a \) and \( b \) can be assigned in any order (the smaller side can be \( a \) or \( b \)), you can have:
- If you assign \( a = 9 \), then \( b = 12 \).
- If you assign \( a = 12 \), then \( b = 9 \).
Since the question asks for the value of \( a \), the possible correct values of \( a \) from the given options are either 9 or 12. You can choose either based on the specific ordering of the triangle sides.
Therefore, the possible correct responses could be:
- \( a = 9 \)
- \( a = 12 \)
Choose either of those two options based on the context of the question. If only one can be selected, use \( a = 9 \) as one of the standard assignments for a right triangle where \( a \) is the shortest side.