document.write( "Question 1103865: A horse breeder wants to construct a RECTANGULAR corral next to a
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\n" ); document.write( "side of the corral as shown in the figure above. The breeder has
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Algebra.Com's Answer #718574 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "We might as well put the barn at the bottom corner\r\n" );
document.write( "of the corral.  \r\n" );
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document.write( "We can get the answer very easily, since of all rectangles,\r\n" );
document.write( "a square has the maximum area for any given perimeter.  The\r\n" );
document.write( "side of the barn adds 16' to the 280' of fencing, making the \r\n" );
document.write( "perimeter 296'.  So since the corral is a square, then each \r\n" );
document.write( "side would be 296' divided by 4 or y=74'.  However your teacher\r\n" );
document.write( "would not accept that reasoning since no algebra is involved.\r\n" );
document.write( "So I'll do it another way using algebra.\r\n" );
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document.write( "The area of the corral is \r\n" );
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document.write( "A = y(x+16)\r\n" );
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document.write( "and the fence, adding up the four parts is\r\n" );
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document.write( "(x)+(y)+(x+16)+(y) = 280\r\n" );
document.write( "        x+y+x+16+y = 280\r\n" );
document.write( "          2x+2y+16 = 280\r\n" );
document.write( "             2x+2y = 264  <--divide through by 2\r\n" );
document.write( "               x+y = 132\r\n" );
document.write( "                 y = 132-x\r\n" );
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document.write( "So A = y(x+16) become\r\n" );
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document.write( "   A = (132-x)(x+16)\r\n" );
document.write( "   A = 132x+2112-x2-16x\r\n" );
document.write( "   A = -x2+116x+2112\r\n" );
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document.write( "This is a parabola that opens down. So its vertex\r\n" );
document.write( "will be a maximum. The formula for the x-value of the \r\n" );
document.write( "vertex is \r\n" );
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document.write( "x = -b/(2a) = (-116)/[2(-1)] =  58\r\n" );
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document.write( "Therefore y = 132-x = 132-58 = 74, so the corral is\r\n" );
document.write( "a 74 ft x 74 ft square, as we got without algebra above.\r\n" );
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document.write( "Edwin
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