document.write( "Question 795518: IN AN EQUILATERAL TRIANGLE ABC,AN IS PERPENDICULAR TO BC. PROVE THAT (AN)SQURE=3(BN)SQUARE. \n" ); document.write( "

Algebra.Com's Answer #481041 by rothauserc(4718) $\"\"$ $\"About$

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For this triangle, Pythagorean theorem states that
\n" ); document.write( "(AN)^2 + (BN)^2 = (AB)^2
\n" ); document.write( "subtract (BN)^2 from both sides of =
\n" ); document.write( "(AN)^2 = (AB)^2 - (BN)^2
\n" ); document.write( "since triangle ABC is equilateral, perpendicular segment AN to BC bisects line segament BC, therefore
\n" ); document.write( "AB = 2BN and
\n" ); document.write( "(AN)^2 = (2BN)^2 - (BN)^2
\n" ); document.write( "(AN)^2 = 4(BN)^2 - (BN)^2
\n" ); document.write( "(AN)^2 = 3(BN)^2
\n" ); document.write( " \n" ); document.write( "

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