jmc

Rectangle $ABCD$ has sides $\overline{AB}$ of length 4 and $\overline{CB}$ of length 3. Divide $\overline{AB}$ into 168 congruent segments with points $A=P_0,P_1,\dots ,P_{168}=B$, and divide $\overline{CB}$ into 168 congruent segments with points $C=Q_0,Q_1,\dots ,Q_{168}=B$. For $1\le k\le 167$, draw the segments $\overline{P_k{Q}_k}$. Repeat this construction on the sides $\overline{AD}$ and $\overline{CD}$, and then draw the diagonal $\overline{AC}$. Find the sum of the lengths of the 335 parallel segments drawn.