Given right ~\triangle ABC~ △ABC space, triangle, A, B, C, space with ~AC=8~ AC=8 space, A, C, equals, 8, space and ~BC=10\, BC=10space, B, C, equals, 10: A rectangle is constructed in ~\triangle ABC~ △ABC space, triangle, A, B, C, space as shown in the diagram. What are the dimensions of the rectangle that would minimize the rectangle's perimeter?