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$