document.write( "Question 1151596: A triangle ABC has sides AB=90 cm and AC=120 cm. A line segment DE is formed such that D lies on side AB while E lies on side AC. If the ratio of the areas of two triangles is 3:5, how far is E from C if AD measures 60 cm? \n" ); document.write( "

Algebra.Com's Answer #773423 by ikleyn(52908) $\"\"$ $\"About$

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document.write( "Start from the formula for the triangle area\r\n" );
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document.write( "      A = ,\r\n" );
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document.write( "where \"a\" and \"b\" are the lengths of any two sides of a triangle and  is the concluded angle between these sides.\r\n" );
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document.write( "For triangle ABC you have then   = .\r\n" );
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document.write( "For triangle ADE you have    = .\r\n" );
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document.write( "Now make the ratio of the triangles areas. You will get this equation \r\n" );
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document.write( "     =  = .\r\n" );
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document.write( "From this equation (this proportion)\r\n" );
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document.write( "    | AE | =  = 108.\r\n" );
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document.write( "So, now you know the length of the segment AE: it is 108 centimeters.\r\n" );
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document.write( "It implies that the length of EC is 120 - 108 = 12 centimeters.\r\n" );
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document.write( "ANSWER.  The distance from E to C is 12 centimeters.\r\n" );
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