document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1121096>Question 1121096</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a triangle ABC, D is a point on side AB and E is the point on AC.<BR>\n" );
document.write( "DE parallel to BC. DE= 1/3 BC.<BR>\n" );
document.write( "Construct a line from D to C.<BR>\n" );
document.write( "Area of triangle ADE is 20cm²<BR>\n" );
document.write( "Find the area of triangle DEC? </SPAN>\n" );
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document.write( "Triangles ADE and ABC are similar; DE = (1/3)*BC, so the ratio of similarity is 1:3.<br><BR>\n" );
document.write( "The ratio of areas is then the square of that, 1:9.<br><BR>\n" );
document.write( "Given that the area of triangle ADE is 20, the area of triangle ABC is then 20*9 = 180.<br><BR>\n" );
document.write( "AD and AB are corresponding sides of the similar triangles, so AD = (1/3)*AB.  That means the area of triangle ADC is (1/3) the area of triangle ABC, because the heights of the two triangles (the perpendicular distance from line AB to point C) are the same.<br><BR>\n" );
document.write( "So the area of triangle ADC is (1/3)*180 = 60.<br><BR>\n" );
document.write( "Finally, the area of triangle DEC is 60-20 = 40.<br><BR>\n" );
document.write( "Answer: The area of triangle DEC is 40 cm^2. </SPAN>\n" );
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