Question 2
Rectangle $ABCD$ has sides $\overline{AB}$ of length $4$ and $\overline{CB}$ of length $3.$ Divide $\overline{AB}$ into $168$ congruent segments with points $A=P_0,$ $P_1,$ $\ldots,$ $P_{168}=B,$ and divide $\overline{CB}$ into $168$ congruent segments with points $C=Q_0,$ $Q_1,$ $\ldots,$ $Q_{168}=B.$ For $1\leq k\leq167,$ draw the segments $\overline{P_kQ_k}.$ 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.