Difference between revisions of "1987 AHSME Problems/Problem 30"
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In the figure, <math>\triangle ABC</math> has <math>\angle A =45^{\circ}</math> and <math>\angle B =30^{\circ}</math>. A line <math>DE</math>, with <math>D</math> on <math>AB</math> | In the figure, <math>\triangle ABC</math> has <math>\angle A =45^{\circ}</math> and <math>\angle B =30^{\circ}</math>. A line <math>DE</math>, with <math>D</math> on <math>AB</math> | ||
and <math>\angle ADE =60^{\circ}</math>, divides <math>\triangle ABC</math> into two pieces of equal area. | and <math>\angle ADE =60^{\circ}</math>, divides <math>\triangle ABC</math> into two pieces of equal area. | ||
| − | (Note: the figure may not be accurate; perhaps <math>E</math> is on <math>CB</math> instead of <math>AC</math> | + | (Note: the figure may not be accurate; perhaps <math>E</math> is on <math>CB</math> instead of <math>AC.) </math> |
The ratio <math>\frac{AD}{AB}</math> is | The ratio <math>\frac{AD}{AB}</math> is | ||
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\textbf{(D)}\ \frac{1}{\sqrt[3]{6}}\qquad | \textbf{(D)}\ \frac{1}{\sqrt[3]{6}}\qquad | ||
\textbf{(E)}\ \frac{1}{\sqrt[4]{12}} </math> | \textbf{(E)}\ \frac{1}{\sqrt[4]{12}} </math> | ||
| − | |||
== See also == | == See also == | ||
Revision as of 08:56, 23 October 2014
Problem
In the figure, 
has 
and 
. A line 
, with 
on 
and 
, divides into two pieces of equal area.
(Note: the figure may not be accurate; perhaps 
is on 
instead of 
The ratio 
is
![[asy] size((220)); draw((0,0)--(20,0)--(7,6)--cycle); draw((6,6)--(10,-1)); label("A", (0,0), W); label("B", (20,0), E); label("C", (7,6), NE); label("D", (9.5,-1), W); label("E", (5.9, 6.1), SW); label("$45^{\circ}$", (2.5,.5)); label("$60^{\circ}$", (7.8,.5)); label("$30^{\circ}$", (16.5,.5)); [/asy]](http://latex.artofproblemsolving.com/1/3/5/135a648963b48464cdd989019e3de4847a416079.png)
![$\textbf{(A)}\ \frac{1}{\sqrt{2}} \qquad \textbf{(B)}\ \frac{2}{2+\sqrt{2}} \qquad \textbf{(C)}\ \frac{1}{\sqrt{3}} \qquad \textbf{(D)}\ \frac{1}{\sqrt[3]{6}}\qquad \textbf{(E)}\ \frac{1}{\sqrt[4]{12}}$](http://latex.artofproblemsolving.com/0/5/5/0552faf8dc8fb3fefe89900cae35dfc47f52ce06.png)
See also
| 1987 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 29 |
Followed by Last Question | |
| 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. 
