MathDB
Perpendicular Medians in a Triangle

Source:

January 18, 2009
geometry

Problem Statement

Medians BD BD and CE CE of triangle ABC ABC are perpendicular, BD \equal{} 8, and CE \equal{} 12. The area of triangle ABC ABC 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("AA",A,S);label("BB",B,N);label("CC",C,S);label("DD",D,S);label("EE",E,NW);label("GG",G,NE); draw(A--B--C--cycle); draw(B--D); draw(E--C); draw(rightanglemark(C,G,D,3));[/asy]<spanclass=latexbold>(A)</span> 24<spanclass=latexbold>(B)</span> 32<spanclass=latexbold>(C)</span> 48<spanclass=latexbold>(D)</span> 64<spanclass=latexbold>(E)</span> 96 <span class='latex-bold'>(A)</span>\ 24\qquad <span class='latex-bold'>(B)</span>\ 32\qquad <span class='latex-bold'>(C)</span>\ 48\qquad <span class='latex-bold'>(D)</span>\ 64\qquad <span class='latex-bold'>(E)</span>\ 96