document.write( "Question 1151146: In the figure to the bottom, DE divides the area of triangle ABC in half. Find the length of EC in m. \r
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Algebra.Com's Answer #772800 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Triangle ABC is a right-angled triangle.\r\n" );
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document.write( "Its leg AB is   = 24 meters long.\r\n" );
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document.write( "Its area is   = 7*12 = 84 square meters.\r\n" );
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document.write( "Triangles ABC and EDC are similar (since they both are right-angled and have common acute angle C).\r\n" );
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document.write( "Hence, their corresponding sides are proportional.\r\n" );
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document.write( "In particular,  EC = k*AC = 24k,  ED = k*AB = 7k,  where \"k\" is the proportionality coefficient.\r\n" );
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document.write( "Then the area of the triangle EDC is   =  = .\r\n" );
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document.write( "It is half the area of the triangle ABC, i.e.\r\n" );
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document.write( "      =  = 42,   or\r\n" );
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document.write( "      =  = .\r\n" );
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document.write( "Therefore, the proportionality coefficient (the similarity coefficient)\r\n" );
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document.write( "     k =  = .\r\n" );
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document.write( "It implies  EC = k*AC =  =  = 16.971 (approximately).    ANSWER\r\n" );
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