document.write( "Question 1101805: What is the area of a rectangle whose perimeter is 92 and the diagonal of 34. \n" ); document.write( "

Algebra.Com's Answer #716426 by ikleyn(52800) $\"\"$ $\"About$

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document.write( "Let x and y be the dimensions of the rectangle.\r\n" );
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document.write( "2x + 2y = 92,   hence\r\n" );
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document.write( " x + y = 46.               (1)\r\n" );
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document.write( "The second equation is\r\n" );
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document.write( " = 34,   or\r\n" );
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document.write( "x^2 + y^2 = 34^2           (2)\r\n" );
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document.write( "Square both sides of eq(1). You will get\r\n" );
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document.write( "x^2 + 2xy + y^2 = 46^2.    (3)\r\n" );
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document.write( "Now subtract eq(2) from eq(3) (both sides).  The terms  x^2  and  y^2 will cancel each other, and you will get\r\n" );
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document.write( "2xy = 46^2 - 34^2  =  (46-34)*(46+34) = 12*80.\r\n" );
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document.write( "Hence,  xy =  = 6*80 = 480.\r\n" );
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document.write( "It is the area of the rectangle, which is under the question.\r\n" );
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document.write( "Answer.  The area of the rectangle is 480 square units.\r\n" );
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