1991 AIME Problems/Problem 2

Problem

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.

Solution

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1991 AIME (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15
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1991 AIME Problems/Problem 2

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