1. The problem is to find the length of the third side (hypotenuse) of a right triangle with legs 3 and 4. 2. Use the Pythagorean theorem: $$a^2 + b^2 = c^2$$ where $a$ and $b$ are the legs and $c$ is the hypotenuse. 3. Substitute the given values: $$3^2 + 4^2 = c^2$$ 4. Calculate squares: $$9 + 16 = c^2$$ 5. Add: $$25 = c^2$$ 6. Take the square root of both sides: $$c = \sqrt{25}$$ 7. Simplify the square root: $$c = 5$$ 8. Therefore, the length of the third side (hypotenuse) is 5.