1. The problem is to find the length of the hypotenuse $x$ in a right triangle where one leg is 6 and the other leg (base) is 3. 2. We use the Pythagorean theorem which states that in a right triangle, the square of the hypotenuse $x$ is equal to the sum of the squares of the other two legs: $$x^2 = a^2 + b^2$$ 3. Substitute the given values: $$x^2 = 6^2 + 3^2$$ 4. Calculate the squares: $$x^2 = 36 + 9$$ 5. Simplify the sum: $$x^2 = 45$$ 6. Take the square root of both sides to solve for $x$: $$x = \sqrt{45}$$ 7. Simplify the square root: $$x = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5}$$ 8. Approximate the value to the nearest tenth: $$x \approx 3 \times 2.236 = 6.7$$ Final answer: $x \approx 6.7$