Difference between revisions of "1991 AHSME Problems/Problem 29"
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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 <math>A</math> now rests at <math>A'</math> on side <math>BC</math>. If <math>BA'=1</math> and <math>A'C=2</math> then the length of the crease <math>PQ</math> is | 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 <math>A</math> now rests at <math>A'</math> on side <math>BC</math>. If <math>BA'=1</math> and <math>A'C=2</math> then the length of the crease <math>PQ</math> is | ||
(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> | ||
| − | {{MAA Notice}} | + | |
| + | == Solution == | ||
| + | <math>\fbox{}</math> | ||
| + | |||
| + | == See also == | ||
| + | {{AHSME box|year=1991|num-b=28|num-a=30}} | ||
| + | |||
| + | [[Category: Intermediate Algebra Problems]] | ||
| + | {{MAA Notice}}Geometry | ||
Revision as of 01:55, 28 September 2014
Problem
Equilateral triangle 
has 
on 
and 
on 
. The triangle is folded along 
so that vertex 
now rests at 
on side 
. If 
and 
then the length of the crease is
(A) 
(B) 
(C) 
(D) 
(E) 
Solution
See also
| 1991 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 28 |
Followed by Problem 30 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
Geometry
