Final answer:
Using the Pythagorean theorem for an isosceles right triangle with a hypotenuse of 6√2, the length of each leg is found to be 3√2.
Step-by-step explanation:
If the hypotenuse of an isosceles right triangle is 6√2, the length of each leg can be found using the Pythagorean theorem, which is a² + b² = c². Since it is an isosceles right triangle, we know both legs are of equal length, so we can call them 'a' and 'a', replacing 'b' in the formula with 'a' to get 2a² = c². Substituting the hypotenuse value into the equation we get 2a² = (6√2)². Solving for 'a', we find a² = 18, and thus a = √18, which simplifies to 3√2.
Therefore, the length of each leg is 3√2.