2002 AMC 12P Problem 24

Let ABCD be a regular tetrahedron and Let E be a point inside the face ABC. Denote by s the sum of the distances from E to the faces DAB, DBC, DCA, and by S the sum of the distances from E to the edges AB, BC, CA. Then \frac{s}{S} equals

\text{(A) }\sqrt{2} \qquad \text{(B) }\frac{2 \sqrt{2}}{3} \qquad \text{(C) }\frac{\sqrt{6}}{2} \qquad \text{(D) }2 \qquad \text{(E) }3

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.