document.write( "Question 333565: Given: Equilateral triangle ABC
\n" ); document.write( "Let D be a point on BC such that BD = \"1%2F3\"BC\r
\n" ); document.write( "\n" ); document.write( "Prove that 9*AD² = 7*AB² \n" ); document.write( "
Algebra.Com's Answer #239013 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Given: Equilateral triangle ABC \r\n" );
document.write( "Let D be a point on BC such that BD = \"1%2F3\"BC\r\n" );
document.write( "\r\n" );
document.write( "Prove that 9*AD² = 7*AB² \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Let BD be 1 unit long, then BC is 3 units long which\r\n" );
document.write( "means that DC is 2 units long, BD = \"1%2F3\"BC.\r\n" );
document.write( "And since triangle ABC is equilateral, \r\n" );
document.write( "AB = AC = BC = 3 and angle B = 60°\r\n" );
document.write( "Let AD = x.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "I am going to assume that you have had the law of cosines.  If\r\n" );
document.write( "you have not studied that yet, then post again, or email me\r\n" );
document.write( "and I will show you how to do it using only the Pythagorean\r\n" );
document.write( "theorem.\r\n" );
document.write( "\r\n" );
document.write( "Using the law of cosines on triangle ABD:\r\n" );
document.write( "\r\n" );
document.write( "AD² = AB² + BD² - 2(AB)(BD)cos(B)\r\n" );
document.write( "\r\n" );
document.write( " x² = 3² + 1² - 2(3)(1)cos(60°)\r\n" );
document.write( "\r\n" );
document.write( " x² = 9 + 1 - 6(.5)\r\n" );
document.write( "\r\n" );
document.write( " x² = 10 - 3\r\n" );
document.write( "\r\n" );
document.write( " x² = 7 \r\n" );
document.write( "\r\n" );
document.write( "AD² = 7\r\n" );
document.write( "\r\n" );
document.write( "9*AD² = 9*7 = 63\r\n" );
document.write( "\r\n" );
document.write( "AB = 3\r\n" );
document.write( "\r\n" );
document.write( "7*AB² = 7*3^2 = 7*9 = 63.\r\n" );
document.write( "\r\n" );
document.write( "So 9*AD² = 7*AB² since both = 63.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "
\n" );