To determine if a triangle with sides 15, 10, and 12 is a right triangle using the Converse of the Pythagorean Theorem, we first need to identify the longest side, which is 15 in this case.
According to the Pythagorean Theorem, for a triangle with sides \( a \), \( b \), and \( c \) (where \( c \) is the longest side), it is a right triangle if \( a^2 + b^2 = c^2 \).
Let's assign the sides:
- \( a = 10 \)
- \( b = 12 \)
- \( c = 15 \)
Now calculate \( a^2 + b^2 \) and \( c^2 \):
- \( a^2 + b^2 = 10^2 + 12^2 = 100 + 144 = 244 \)
- \( c^2 = 15^2 = 225 \)
Now, compare \( a^2 + b^2 \) to \( c^2 \):
- \( 244 \) is not equal to \( 225 \).
Since \( a^2 + b^2 \neq c^2 \), we conclude that the triangle with sides 15, 10, and 12 is not a right triangle.
Thus, the correct response is: No, because 244 is not equal to 225.