The problem requires solving for $x$ in an isosceles right triangle with the hypotenuse given as $8\sqrt{2}$ cm.

Step-by-Step Solution:

1. In an isosceles right triangle, the two legs are equal, and the hypotenuse is related to the legs by the Pythagorean theorem: $c = x\sqrt{2}$ where $c$ is the hypotenuse, and $x$ is the length of each leg.

2. Substituting the given hypotenuse $c = 8\sqrt{2}$ into the formula: $8\sqrt{2} = x\sqrt{2}$

3. Solve for $x$: Divide both sides by $\sqrt{2}$: $x = 8$

Final Answer:

$x = 8$

Would you like additional details or clarification?

Related Questions:

1. How does the Pythagorean theorem apply to isosceles right triangles?
2. What are the key properties of 45°-45°-90° triangles?
3. How do you simplify expressions with square roots in equations?
4. Can you calculate the perimeter of this triangle with the given hypotenuse?
5. How does the ratio of side lengths differ between different types of triangles?

Tip: For isosceles right triangles, remember the ratio of leg to hypotenuse is always $1 : \sqrt{2}$.