Answer:
A triangle is a right triangle if the square of the length of the longest side (the hypotenuse in a right triangle) is equal to the sum of the squares of the lengths of the other two sides. This is known as the Pythagorean theorem, which can be written as:
a² + b² = c²
where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
In this case, the longest side is 12, and the other two sides are 6 and 9. So we can substitute these values into the Pythagorean theorem:
6² + 9² = 12²
36 + 81 = 144
117 = 144
These values are not equal, so the triangle with side lengths 6, 9, and 12 is not a right triangle.