Jean made a piece of stained glass art in the shape of two mountains, as shown in the figure below. One mountain peak is 8 feet high and the other peak is 12 feet high. Each peak forms a 90^\circ angle, and the straight sides of the mountains form 45^\circ angles with the ground. The artwork has an area of 183 square feet. The sides of the mountains meet at an intersection point near the center of the artwork, h feet above the ground. What is the value of h?
Answer Choices
A. 4
B. 5
C. 4\sqrt{2}
D. 6
E. 5\sqrt{2}