document.write( "Question 1094565: Given: Square ABCD with a total area of 64 sq in.
\n" ); document.write( " Point M is in the midpoint of CD to form triangle ADM
\n" ); document.write( " Point N is 5 inches from point C and 3 inches from point B to form triangle NCD\r
\n" ); document.write( "\n" ); document.write( "Question: What is the area shared by triangle ADM and NCD?\r
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Algebra.Com's Answer #709280 by ikleyn(52784) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "The plot to start with is in Figure 1.  The problem asks to find the area of the triangle DEM.\r\n" );
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document.write( "           Figure 1.\r\n" );
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document.write( "           Figure 2.\r\n" );
document.write( " Let x be the area of the triangle DEM, which is under the question.\r\n" );
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document.write( "It is clear that the area of the triangle AMD is 16 square inches.\r\n" );
document.write( "Hence, the area of the triangle AED is 16-x square inches.\r\n" );
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document.write( "Draw the line CG from the vertex C parallel to AM (blue line in Figure 2),\r\n" );
document.write( "and let F be the intersection point of lines CG and DN.\r\n" );
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document.write( "Then it is clear that\r\n" );
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document.write( "   - The triangle DFC is similar to triangle DEM, and the area of the triangle DFC is four times area of the triangle DEM;\r\n" );
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document.write( "   - The triangle CFN is similar to triangle AED, and the similarity coefficient is . So, the area of the triangle CFN is \r\n" );
document.write( "     of the area of the triangle AED, i.e. Area(CFN) = .\r\n" );
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document.write( "   - The area of the triangle DNC is  = 4*5 = 20.\r\n" );
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document.write( "Now the final step of setup is to write the equation for the area of the triangle DNC as the sum of areas of the triangles DFC and CFN:\r\n" );
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document.write( "        4x +  = 20.     (1)\r\n" );
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document.write( "The setup is completed, and I leave it to you to solve the final equation (1) and to get the answer.\r\n" );
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