Algebra.Com's Answer #853442 by ikleyn(53646)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "The perimeter of a rectangle is 40, and the length of one of its diagonals is 10 \sqrt{2}.
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document.write( "Find the area of the rectangle.
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document.write( "Let 'a' and 'b' be the lengths of two adjacent sides of the rectangle.\r\n" );
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document.write( "Then \r\n" );
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document.write( " a + b = 40/2 = 20,\r\n" );
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document.write( " a^2 + b^2 =  = 200.\r\n" );
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document.write( "Thus we have b = 20-a, and we substitute it into the second equation\r\n" );
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document.write( " a^2 + (20-a)^2 = 200,\r\n" );
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document.write( " a^2 + 400 - 40a + a^2 = 200,\r\n" );
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document.write( " 2a^2 - 40a + 200 = 0,\r\n" );
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document.write( " a^2 - 20a + 100 = 0,\r\n" );
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document.write( " (a-10)^2 = 0,\r\n" );
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document.write( " a = 10.\r\n" );
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document.write( "Hence, the rectangle is a square with the side length of 10 units.\r\n" );
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document.write( "Thus the area of this rectangle (square) is 10^2 = 100 square untis.\r\n" );
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document.write( "At this point, the problem is solved completely.\r
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