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?

Question

(1 point)
Responses

a=12
a equals 12

a=15
a equals 15

a=81
a equals 81

a=9

Answer 1

In a right triangle, the sides \( a \) and \( b \) are the legs, and \( c \) is the hypotenuse. For the Pythagorean triple (9, 12, 15), \( c \) is the hypotenuse, which means it is the longest side. Thus, \( c = 15 \) and the legs \( a \) and \( b \) can be either 9 or 12.

Therefore, the correct value of \( a \) can be either 9 or 12. Based on the provided options, the possible value of \( a \) is:

• \( a = 9 \)
• \( a = 12 \)

Since only one of the answers can be chosen, and since both 9 and 12 are valid lengths for the legs, the correct answer to select from the given options is:

a = 9