SOLUTION: Th base of an isosceles triangle is 2 root2 cm. If the medians to the equal sides intersect at right angles, then the height of the triangle, in cm, is

The two intersecting medians and the base of the given triangle form an isosceles right triangle with the hypotenuse of  centimeters.


Hence, the altitude of this isosceles right triangle drawn to its hypotenuse is exactly HALF of the base, i.e.  centimeters.


Next, the length of this altitude is exactly one third of the height of the given triangle; 

so, the height of the given isosceles triangle is  centimeters.    ANSWER