Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10, and 12 is a right triangle.
A: No, because 325 is not equal to 144.
B: No, because 22 is not equal to 15.
C: No, because 244 is not equal to 225.
D: No, because 369 is not equal to 100.
To determine whether a triangle with sides 15, 10, and 12 is a right triangle, we can use the converse of the Pythagorean Theorem, which states that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.
In this case, the longest side is 15. We can calculate the values on both sides of the equation:
15^2 = 225
10^2 + 12^2 = 100 + 144 = 244
Since 225 is not equal to 244, the triangle with sides 15, 10, and 12 is not a right triangle.
Therefore, the correct answer is C: No, because 244 is not equal to 225.