1. The problem is to find the value of $x$ in a right triangle where the vertical side is 2, the horizontal side is 10, and $x$ is the hypotenuse. 2. According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse ($x$) is equal to the sum of the squares of the other two sides. 3. Write the equation: $$x^2 = 2^2 + 10^2$$ 4. Calculate the squares: $$x^2 = 4 + 100$$ 5. Sum the values: $$x^2 = 104$$ 6. Take the square root of both sides to solve for $x$: $$x = \sqrt{104}$$ 7. Simplify the square root if possible: $$x = \sqrt{4 \times 26} = 2\sqrt{26}$$ 8. Therefore, the value of $x$ is $2\sqrt{26}$.