1. **Problem Statement:** We have an isosceles right triangle with an altitude drawn from the right angle vertex to the hypotenuse. The altitude length is $x$ units. We need to find the length of one leg of the large right triangle in terms of $x$. 2. **Key Properties:** In an isosceles right triangle, the legs are congruent, and the hypotenuse is $\sqrt{2}$ times the length of each leg. 3. **Setup:** Let the length of each leg be $a$. The hypotenuse is then $a\sqrt{2}$. 4. **Altitude in Right Triangle:** The altitude to the hypotenuse in a right triangle can be found using the formula: $$\text{altitude} = \frac{\text{product of legs}}{\text{hypotenuse}}$$ 5. Substitute values: $$x = \frac{a \times a}{a\sqrt{2}} = \frac{a^2}{a\sqrt{2}}$$ 6. Simplify the fraction: $$x = \frac{a^2}{a\sqrt{2}} = \frac{\cancel{a} a}{\cancel{a} \sqrt{2}} = \frac{a}{\sqrt{2}}$$ 7. Solve for $a$: $$a = x \sqrt{2}$$ **Final answer:** The length of one leg of the large right triangle is $x\sqrt{2}$ units.