document.write( "Question 1154271: Square ABCD has 8-inch sides, M is the midpoint of BC, and N is the intersection of AM and diagonal BD. Find the lengths of NB, NM, NA, and ND. \n" ); document.write( "
Algebra.Com's Answer #776691 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Draw PQ through N parallel to AB\r\n" );
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document.write( "\"AP%2F%28MQ%29=PD%2F%28QB%29\"\r\n" );
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document.write( "\"AD=AP%2BPD=8\"     \"MB=MQ%2BQB=4\"\r\n" );
document.write( "   \"PD=8-AP\"        \"QB=4-MQ\"\r\n" );
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document.write( "\"AP%2F%28MQ%29=%288-AP%29%2F%284-MQ%29\"\r\n" );
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document.write( "\"AP%284-MQ%29=MQ%288-AP%29\"\r\n" );
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document.write( "\"4%2AAP-AP%2AMQ=8%2AMQ-MQ%2AAP\"\r\n" );
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document.write( "\"4%2AAP-AP%2AMQ=8%2AMQ-MQ%2AAP\"\r\n" );
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document.write( "\"4%2AAP-AP%2AMQ=8%2AMQ-AP%2AMQ\"\r\n" );
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document.write( "\"4%2AAP=8%2AMQ\"\r\n" );
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document.write( "\"AP=2%2AMQ\"\r\n" );
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document.write( "By similar triangles,\r\n" );
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document.write( "\"NA=2%2ANM\"\r\n" );
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document.write( "By the Pythagorean theorem,\r\n" );
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document.write( "\"AM%5E2=AB%5E2%2BBM%5E2\"\r\n" );
document.write( "\"AM%5E2=8%5E2%2B4%5E2\"\r\n" );
document.write( "\"AM%5E2=64%2B16\"\r\n" );
document.write( "\"AM%5E2=80\"\r\n" );
document.write( "\"AM=sqrt%2880%29\"\r\n" );
document.write( "\"AM=sqrt%2816%2A5%29\"\r\n" );
document.write( "\"AM=4sqrt%285%29\"\r\n" );
document.write( "\"NA%2BNM=4sqrt%285%29\"\r\n" );
document.write( "\"2%2ANM%2BNM=4sqrt%285%29\"\r\n" );
document.write( "\"3%2ANM=4sqrt%285%29\"\r\n" );
document.write( "\"NM=4sqrt%285%29%2F3\"\r\n" );
document.write( "\"NA=2%2ANM=2%2A4sqrt%285%29%2F3=8sqrt%285%29%2F3\"\r\n" );
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document.write( "You finish by finding NB and ND the same way.\r\n" );
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document.write( "Edwin

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