1. **State the problem:** We have a right triangle with legs of length $x$ and $x$, and the hypotenuse is $3\sqrt{2}$. We need to find the value of $x$ in simplest form. 2. **Formula used:** In a right triangle, by the Pythagorean theorem, the square of the hypotenuse equals the sum of the squares of the legs: $$c^2 = a^2 + b^2$$ Here, $c = 3\sqrt{2}$, and both legs are equal, so $a = b = x$. 3. **Apply the formula:** $$ (3\sqrt{2})^2 = x^2 + x^2 $$ $$ 9 \times 2 = 2x^2 $$ $$ 18 = 2x^2 $$ 4. **Solve for $x^2$:** $$ \cancel{2} \times 9 = \cancel{2} x^2 $$ $$ 9 = x^2 $$ 5. **Find $x$:** $$ x = \sqrt{9} = 3 $$ **Final answer:** $$ x = 3 $$