document.write( "Question 1178962: The area of a garden is 972 square feet, and the length of its diagonal is 45 feet. Find the dimensions of the garden. \n" ); document.write( "

Algebra.Com's Answer #808433 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "The area of a $\"highlight%28rectangular%29\"$ garden is 972 square feet, and the length of its diagonal is 45 feet.
\n" ); document.write( "Find the dimensions of the garden.
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\n" ); document.write( "\n" ); document.write( "            The solution by @Mananth is irrelevant and has nothing in common with the problem.\r
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\n" ); document.write( "\n" ); document.write( "            For your safety, simply IGNORE HIS (or her) POST.\r
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\n" ); document.write( "\n" ); document.write( "            I came to bring the correct solution.\r
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\n" ); document.write( "\n" ); document.write( "            Notice how I edited the condition in order for the problem would make sense.\r
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document.write( "Let x be the larger dimension of the rectangle, \r\n" );
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document.write( "and let y be its smaller dimension.\r\n" );
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document.write( "Then we have these two equations from the condition\r\n" );
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document.write( "    xy = 972            (1)\r\n" );
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document.write( "     = 45.    (2)\r\n" );
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document.write( "From equations (1) and (2), you get\r\n" );
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document.write( "    x^2 + 2xy + y^2 =  + 2*972 = 3969 = \r\n" );
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document.write( "    x^2 - 2xy + y^2 =  - 2*972 =   81 = .\r\n" );
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document.write( "It can be simplified to\r\n" );
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document.write( "    x + y = 63\r\n" );
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document.write( "    x - y =  9\r\n" );
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document.write( "It implies  2x = 63+ 9 = 72;  x = 36;  y = 27.\r\n" );
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document.write( "ANSWER.  The dimensions of the rectangle are 36 feet and  27 feet.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved (correctly).\r
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