Difference between revisions of "1991 AIME Problems/Problem 2"
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== Problem == | == Problem == | ||
| + | Rectangle <math>ABCD_{}^{}</math> has sides <math>\overline {AB}</math> of length 4 and <math>\overline {CB}</math> of length 3. Divide <math>\overline {AB}</math> into 168 congruent segments with points <math>A_{}^{}=P_0, P_1, \ldots, P_{168}=B</math>, and divide <math>\overline {CB}</math> into 168 congruent segments with points <math>C_{}^{}=Q_0, Q_1, \ldots, Q_{168}=B</math>. For <math>1_{}^{} \le k \le 167</math>, draw the segments <math>\overline {P_kQ_k}</math>. Repeat this construction on the sides <math>\overline {AD}</math> and <math>\overline {CD}</math>, and then draw the diagonal <math>\overline {AC}</math>. Find the sum of the lengths of the 335 parallel segments drawn. | ||
== Solution == | == Solution == | ||
| + | {{solution}} | ||
== See also == | == See also == | ||
| − | + | {{AIME box|year=1991|num-b=1|num-a=3}} | |
Revision as of 01:02, 2 March 2007
Problem
Rectangle 
has sides 
of length 4 and 
of length 3. Divide into 168 congruent segments with points 
, and divide into 168 congruent segments with points 
. For 
, draw the segments 
. Repeat this construction on the sides 
and 
, and then draw the diagonal 
. Find the sum of the lengths of the 335 parallel segments drawn.
Solution
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See also
| 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 | ||
| All AIME Problems and Solutions | ||
