1. The problem is to find the hypotenuse of a right-angled triangle given the lengths of the base and perpendicular sides. 2. The formula used is the Pythagorean theorem: $$\text{Hypotenuse}^2 = \text{Base}^2 + \text{Perpendicular}^2$$ 3. Important rule: The hypotenuse is the longest side opposite the right angle. 4. Example: Given base = 3 cm and perpendicular = 4 cm, calculate the hypotenuse. 5. Substitute values: $$\text{Hypotenuse}^2 = 3^2 + 4^2$$ 6. Calculate squares: $$\text{Hypotenuse}^2 = 9 + 16$$ 7. Add: $$\text{Hypotenuse}^2 = 25$$ 8. Take square root: $$\text{Hypotenuse} = \sqrt{25} = 5$$ 9. Therefore, the hypotenuse is 5 cm.