Difference between revisions of "1991 AHSME Problems/Problem 29"

(Created page with "Equilateral triangle <math>ABC</math> has <math>P</math> on <math>AB</math> and <math>Q</math> on <math>AC</math>. The triangle is folded along <math>PQ</math> so that vertex <ma...")
 
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(A) <math>\frac{8}{5}</math> (B) <math>\frac{7}{20}\sqrt{21}</math> (C) <math>\frac{1+\sqrt{5}}{2}</math> (D) <math>\frac{13}{8}</math> (E) <math>\sqrt{3}</math>
 
(A) <math>\frac{8}{5}</math> (B) <math>\frac{7}{20}\sqrt{21}</math> (C) <math>\frac{1+\sqrt{5}}{2}</math> (D) <math>\frac{13}{8}</math> (E) <math>\sqrt{3}</math>
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Revision as of 12:54, 5 July 2013

Equilateral triangle $ABC$ has $P$ on $AB$ and $Q$ on $AC$. The triangle is folded along $PQ$ so that vertex $A$ now rests at $A'$ on side $BC$. If $BA'=1$ and $A'C=2$ then the length of the crease $PQ$ is

(A) $\frac{8}{5}$ (B) $\frac{7}{20}\sqrt{21}$ (C) $\frac{1+\sqrt{5}}{2}$ (D) $\frac{13}{8}$ (E) $\sqrt{3}$ The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png