Find the leg of each isosceles right triangle when the hypotenuse is of the given measure.
given = 6sqre root two cm

In any right triangle,

      (Hypotenuse)²  =  (one leg)²  +  (other leg)² .

In an isosceles right triangle, the legs have equal lengths, so  

       (Hypotenuse)²  =  (leg)²  +  (leg)² .

       (Hypotenuse)²  =   2 (leg)² .

         Hypotenuse = √(2 leg²)

         Hypotenuse  =  leg √2 .

In this particular isosceles right triangle,

         Hypotenuse = 6 √2 cm.

                leg √2  =  6 √2

                leg       =  6  cm    

Cis your correct answer