AHSME 1968 Problem 31

In this diagram, not drawn to scale, Figures $I$ and $III$ are equilateral triangular regions with respective areas of $32\sqrt{3}$ and $8\sqrt{3}$ square inches. Figure $II$ is a square region with area $32$ square inches. Let the length of segment $AD$ be decreased by $12\tfrac{1}{2}$ % of itself, while the lengths of $AB$ and $CD$ remain unchanged. The percent decrease in the area of the square is: $\text{(A)}\ 12\tfrac{1}{2} \text{(B)}\ 25 \text{(C)}\ 50 \text{(D)}\ 75 \text{(E)}\ 87\tfrac{1}{2}$