Final answer:
The length of the third side of a right-angled triangle can be found using the Pythagorean theorem. In this case, there is only one possibility for the length of the third side, which is approximately 7.81cm.
Step-by-step explanation:
In a right-angled triangle, the length of the third side can be found using the Pythagorean theorem. The theorem states that the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the hypotenuse.
In this case, the two shorter sides are 5cm and 6cm. Let's call the third side x. Using the Pythagorean theorem, we have 5² + 6² = x². Simplifying, we get 25 + 36 = x². Combining like terms, we get 61 = x². Taking the square root of both sides, we find that x ≈ 7.81. Therefore, there is only one possibility for the length of the third side, which is approximately 7.81cm.