page 15 of 15 Pythagorean Triples Quick Check 4 of 54 of 5 Items Question Use the image to answer the question. Given is a right triangle with side lengths a, b, and c. The Pythagorean triple (9,12,15) represents the side lengths of the given right triangle. Which of the following is the correct value of a? (1 point) Responses a=81 a equals 81 a=15 a equals 15 a=12 a equals 12 a=9 a equals 9 Skip to navigation

1 answer

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.