AMC8 2002 Problem 16

Right isosceles triangles are constructed on the sides of a 3-4-5 right triangle, as shown. A capital letter represents the area of each triangle. Which one of the following is true?
Image
Answer Choices
A. X+Z=W+Y
B. W+X=Z
C. 3 X+4 Y=5 Z
D. X+W=\dfrac{1}{2}(Y+Z)
E. X+Y=Z