document.write( "Question 1187952: Solve the given problem.\r
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Algebra.Com's Answer #818969 by ikleyn(52852) $\"\"$ $\"About$

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\n" ); document.write( "The area of a rectangle is 48 square meters. Find its dimension if the shorter side is four less than the diagonal.
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document.write( "Let x and y be the sides of the rectangle.\r\n" );
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document.write( "Then from the description, we have these two equations\r\n" );
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document.write( "    xy = 48                (1)     (for the area)\r\n" );
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document.write( "and\r\n" );
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document.write( "    x^2 + y^2 = (x+4)^2    (2)      (for the diagonal)\r\n" );
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document.write( "From equation (2), we have\r\n" );
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document.write( "    x^2 + y^2 = x^2 + 8x + 16,\r\n" );
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document.write( "          y^2 =       8x + 16.    (3)\r\n" );
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document.write( "Now we square both sides of the equation (1)\r\n" );
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document.write( "    x^2 * y^2 = 48^2              (4)\r\n" );
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document.write( "and substitute expression (3) into equation (4), replacing y^2 there.  We get then\r\n" );
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document.write( "    x^2 * (8x + 16) = 48^2\r\n" );
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document.write( "Cancel common factor 8 in both side.  You get\r\n" );
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document.write( "    x^2 * (x + 2) = 48*6,\r\n" );
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document.write( "or\r\n" );
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document.write( "    x*2 * (x + 2) = 288.\r\n" );
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document.write( "It is easy to solve MENTALLY in your head by \"trying and error\" :  x = 6.\r\n" );
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document.write( "Indeed, 6^2 * (6+2) = 36*8 = 288.\r\n" );
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document.write( "So, the dimensions of the rectangle are 6 and  = 8 meters.\r\n" );
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document.write( "You may check it on your own that all conditions of the problem are satisfied.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved and explained in all details.\r
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\n" ); document.write( "\n" ); document.write( "Do not forget to post your \" THANKS \" to me for my teaching.\r
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\n" ); document.write( "\n" ); document.write( "As I understand, this problem is posted as a replacement of the yesterday's problem\r
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\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1187886.html\r
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\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1187886.html\r
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\n" ); document.write( "\n" ); document.write( "which I classified / diagnosed as a mistakable . . . \r
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