A right-angled triangle has sides of 8 cm and 15 cm. Calculate the hypotenuse, perimeter, and area.

In a right-angled triangle, the Pythagorean theorem states that $a^2 + b^2 = c^2$, where $a$ and $b$ are the lengths of the two shorter sides (legs), and $c$ is the length of the hypotenuse (the longest side, opposite the right angle).
Here, the legs are 8 cm and 15 cm, and the hypotenuse is $x$.

The length of the third side is $\boxed{\text{17 cm}}$.

The perimeter is the sum of the lengths of all three sides.
Perimeter $= \text{side}_1 + \text{side}_2 + \text{side}_3$

Perimeter $= 8 \text{ cm} + 15 \text{ cm} + 17 \text{ cm}$
Perimeter $= 40 \text{ cm}$
The perimeter of the triangle is $\boxed{\text{40 cm}}$.

Area $= \frac{1}{2} \times \text{base} \times \text{height}$
In a right-angled triangle, the two legs can be considered the base and height.

Area $= \frac{1}{2} \times 8 \text{ cm} \times 15 \text{ cm}$
Area $= 4 \text{ cm} \times 15 \text{ cm}$
Area $= 60 \text{ cm}^2$
The area of the triangle is $\boxed{\text{60 cm}^2}$.