document.write( "Question 1205822: If line DE = $\"+12+sqrt%28+3+%29+\"$ in the diagram, what is the area of the shaded region?\r
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Algebra.Com's Answer #842863 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Notice that ABC is a right angled triangle with the leg/hypotenuse ratio 36/60 = 3/5;\r\n" );
document.write( "hence, it is 3:4:5 triangle. In particular, its leg AC has the length of 48 units.\r\n" );
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document.write( "              Next, let's continue.\r\n" );
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document.write( "Triangles ABC and EDC are similar.\r\n" );
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document.write( "The corresponding legs are AB and ED.\r\n" );
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document.write( "The coefficient of similarity is the ratio\r\n" );
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document.write( "    k =  =  = .\r\n" );
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document.write( "Hence, the area of triangle EDC is    times the area of triangle ABC\r\n" );
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document.write( "     =  =  =  = 288.\r\n" );
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document.write( "The shaded area is the difference \r\n" );
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document.write( "      -  =  - 288 = 864 - 288 = 576 square units.\r\n" );
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document.write( "At this point, the problem is just solved.\r\n" );
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document.write( "ANSWER.  The shaded area is 576 square units.\r\n" );
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\n" ); document.write( "\n" ); document.write( "There are two major ideas in the solution.\r
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document.write( "First idea is that triangle ABC is 3:4:5 right angled triangle.\r\n" );
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document.write( "      As soon as the student get it, it makes OBVIOUS the fact that \r\n" );
document.write( "      the leg AC is 48 units long, without further calculations.\r\n" );
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document.write( "Second idea is that triangles ABC and EDC are similar. \r\n" );
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document.write( "      It opens a straight way to find the area of triangle EDC.\r\n" );
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document.write( "      The rest of the solution is simple arithmetic.\r\n" );
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document.write( "Good student should see these ideas momentarily, and the rest of the solution\r\n" );
document.write( "should take as much time \r\n" );
document.write( "(or as little time) as needed to write/(to print) the thoughts and the calculations \r\n" );
document.write( "on the paper (or in the screen).\r\n" );
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