document.write( "Question 1166670: Find the height in cm, of trapezoid ABCD
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Algebra.Com's Answer #791295 by ikleyn(52874) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            It was not simple task for me to find the way --- but I found it (!)\r
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\n" ); document.write( "\n" ); document.write( "            Unfortunately, the solution goes through UGLY calculations --- but I do not see other way
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document.write( "1)  We have right angled triangle ABE.  The hypotenuse AB is 61 units long; the leg AE is 60 units long.\r\n" );
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document.write( "    Hence, the leg BE is   = 11.\r\n" );
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document.write( "2)  We have right angled triangle ADE.  The hypotenuse AD is 156 units long; the leg AE is 60 units long.\r\n" );
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document.write( "    Hence, the leg ED is   = 144.\r\n" );
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document.write( "3)  The area of the triangle ABD is   =  =  = 4650 square units.\r\n" );
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document.write( "4)  Triangles ADE and BCD are similar (they are right-angled and have congruent angles DBC and BDA).\r\n" );
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document.write( "    From similarity, we have this proportion \r\n" );
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document.write( "         = ,  or   =  = .\r\n" );
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document.write( "        hence  |DC| = .\r\n" );
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document.write( "5)  Then the area of the triangle BCD  is   =  =  = .\r\n" );
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document.write( "6)  The area of the trapezoid ABCD is the sum of areas of triangles  \r\n" );
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document.write( "         =  +  = 4650 +  =  = .\r\n" );
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document.write( "7)  From the similarity of triangles ADE and BCD we have this proportion\r\n" );
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document.write( "         = ,  or    = \r\n" );
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document.write( "    From the proportion,  |BC| =  =  = 155.\r\n" );
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document.write( "8)  Now the area of the trapezoid ABCD is half sum of its bases AD and BC multiplied by the height of the trapezoid, or\r\n" );
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document.write( "         = .\r\n" );
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document.write( "    It gives  H =  = 59  = 59  = 59 .    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "I hope I deserved your \"THANKS\" for my efforts --- so I am open to accept them (!)\r
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