Difference between revisions of "1997 AHSME Problems/Problem 15"
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Medians <math>BD</math> and <math>AE</math> of triangle <math>ABC</math> are perpendicular, <math>BD=8</math>, and <math>CE=12</math>. The area of triangle <math>ABC</math> is | Medians <math>BD</math> and <math>AE</math> of triangle <math>ABC</math> are perpendicular, <math>BD=8</math>, and <math>CE=12</math>. The area of triangle <math>ABC</math> is | ||
| − | + | <asy> | |
defaultpen(linewidth(.8pt)); | defaultpen(linewidth(.8pt)); | ||
dotfactor=4; | dotfactor=4; | ||
| Line 13: | Line 13: | ||
pair G = intersectionpoint(E--C,B--D); | pair G = intersectionpoint(E--C,B--D); | ||
dot(A);dot(B);dot(C);dot(D);dot(E);dot(G); | dot(A);dot(B);dot(C);dot(D);dot(E);dot(G); | ||
| − | label(" | + | label("$A$",A,S);label("$B$",B,N);label("$C$",C,S);label("$D$",D,S);label("$E$",E,NW);label("$G$",G,NE); |
draw(A--B--C--cycle); | draw(A--B--C--cycle); | ||
draw(B--D); | draw(B--D); | ||
draw(E--C); | draw(E--C); | ||
| − | draw(rightanglemark(C,G,D,3)); | + | draw(rightanglemark(C,G,D,3));</asy> |
<math> \textbf{(A)}\ 24\qquad\textbf{(B)}\ 32\qquad\textbf{(C)}\ 48\qquad\textbf{(D)}\ 64\qquad\textbf{(E)}\ 96 </math> | <math> \textbf{(A)}\ 24\qquad\textbf{(B)}\ 32\qquad\textbf{(C)}\ 48\qquad\textbf{(D)}\ 64\qquad\textbf{(E)}\ 96 </math> | ||
| + | |||
| + | == See also == | ||
| + | {{AHSME box|year=1997|num-b=10|num-a=12}} | ||
Revision as of 10:12, 9 August 2011
Problem
Medians 
and 
of triangle 
are perpendicular, 
, and 
. The area of triangle is
![[asy] defaultpen(linewidth(.8pt)); dotfactor=4; pair A = origin; pair B = (1.25,1); pair C = (2,0); pair D = midpoint(A--C); pair E = midpoint(A--B); pair G = intersectionpoint(E--C,B--D); dot(A);dot(B);dot(C);dot(D);dot(E);dot(G); label("$A$",A,S);label("$B$",B,N);label("$C$",C,S);label("$D$",D,S);label("$E$",E,NW);label("$G$",G,NE); draw(A--B--C--cycle); draw(B--D); draw(E--C); draw(rightanglemark(C,G,D,3));[/asy]](http://latex.artofproblemsolving.com/a/0/f/a0fa86e3c4a1430fc804dcaddd4a346d89ca0c0f.png)
See also
| 1997 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 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 | ||
