The sides of an isosceles right triangle with angles 45-45-90 are in the ratio: 1-1-sqrt(2) with the sqrt(2) as the hypotenuse length.
So, if the hypotenuse is 5 * sqrt(6), then we can solve for the leg of the triangle by doing:
(5 * sqrt(6))/sqrt(2) = (5 * sqrt(12))/2 = (10 * sqrt(3))/2 = 5 * sqrt(3)
The length of one leg of the triangle is 5 square root 3.