document.write( "Question 1148799: The sum of the perimeters of two squares is 80 in., and the area of one is 3 times the area of the other. Find the side length of each square. \n" ); document.write( "

Algebra.Com's Answer #770139 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " The solution by @josgarithmetic is not precisely correct, producing partly absurdist result.\r
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document.write( "Let x be the side length of the larger square and y be that of the smaller square.\r\n" );
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document.write( "    4x + 4y = 80    (1)\r\n" );
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document.write( "    x^2 = 3y^2      (2)\r\n" );
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document.write( "===========================>   \r\n" );
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document.write( "    x + y = 20      (3)\r\n" );
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document.write( "    x^2 = 3y^2      (4)\r\n" );
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document.write( "From (1),  y = 20-x.  Substitute it into (4).  You will get\r\n" );
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document.write( "    x^2 = 3*(20-x)^2\r\n" );
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document.write( "    x^2 = 3*(400 - 40x + x^2)\r\n" );
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document.write( "    x^2 = 1200 - 120x + 3x^2\r\n" );
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document.write( "    2x^2 - 120x + 1200 = 0\r\n" );
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document.write( "    x^2  -  60x + 600 = 0\r\n" );
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document.write( "    x =  =  =  = .\r\n" );
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document.write( "Although the quadratic equation has 2 roots, only smaller value  x=   is the solution to the problem,\r\n" );
document.write( "since the larger value    produces NEGATIVE value of \"y\", due to (3).\r\n" );
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document.write( "ANSWER.  The larger square has the side length   = 12.68 inches, approximately.\r\n" );
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document.write( "         The smaller square has the side length   =  = 7.32 in (approximately).\r\n" );
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