1991 AIME Problem 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_{}^{} \le k \le 167, 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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

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