The shaded region in the figure above represents a frame shaped as a right triangle with sides \( A B \) \( =15 \mathrm{~cm} \) and \( A C=17 \mathrm{~cm} \) . The frame \( A B C \) encloses a picture, shaped also as a right triangle, whose area is \( 1 / 2 \) of the area of the frame. If the sum of the lengths of the two sides of the triangular picture is 14 cm, what is the length of the hypotenuse of the picture?