Final answer:
Given a right triangle with sides 9 cm and 12 cm, the hypotenuse can be calculated using the Pythagorean theorem. The calculated hypotenuse is 15 cm, making the triangle unique.
Step-by-step explanation:
The question is about determining whether the conditions given form a unique triangle or more than one triangle. Given that we have a right triangle with two sides measuring 9 centimeters and 12 centimeters, we can determine the third side using the Pythagorean theorem. This theorem states that for a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let the sides forming the right angle be a and b, and the hypotenuse be c. By the theorem, a2 + b2 = c2. Plugging in the given values, we have 92 + 122 = 81 + 144 = 225. So, c2 = 225, which means c = 15 cm.
Since the sides of the triangle are defined and the triangle adheres to the constraints of the Pythagorean theorem, there exists a unique solution. Hence, these conditions determine a unique triangle.