Final answer:
The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem. In this case, the length of the hypotenuse is 2√17 cm.
Step-by-step explanation:
The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments of 2 cm and 8 cm long. To solve for the length of the hypotenuse, we can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. Let the length of the hypotenuse be 'x', then we have:
2² + 8² = x²
4 + 64 = x²
68 = x²
x = √68 = √4*17 = 2√17 cm