document.write( "Question 1181236: The areas Of the faces Of a right rectangular prism are 6, 9, and 12cm^2.
\n" ); document.write( "a, To the nearest tenth of a centimeter, what is the length of the diagonal of the prism?
\n" ); document.write( "b, what is the volume of the prism? Anser in simplest radical form \n" ); document.write( "

Algebra.Com's Answer #811144 by ikleyn(52814) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            As the problem is worded and presented, it is TERRIBLE.\r
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\n" ); document.write( "\n" ); document.write( "            Nevertheless, I was able to decipher its hidden meaning.\r
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document.write( "Let x, y and z be the three dimensions of the prism.\r\n" );
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document.write( "Then we are given these three equations\r\n" );
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document.write( "    xy = 6    (1)\r\n" );
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document.write( "    xz = 9    (2)\r\n" );
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document.write( "    yz = 12   (3)\r\n" );
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document.write( "Multiply these equations. You will get\r\n" );
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document.write( "    (xyz)^2 = 6*9*12 = 648 = (2*3) * (3*3) * (3*4) = 2 * 3^4 * 4 = 2^3 * 3^4\r\n" );
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document.write( "which implies\r\n" );
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document.write( "     xyz =  =  =  = .    (4)\r\n" );
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document.write( "Now       divide equation (4) by equation (1).  You will get  z =  = .\r\n" );
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document.write( "Next,     divide equation (4) by equation (2).  You will get  y =  = .\r\n" );
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document.write( "Finally,  divide equation (4) by equation (3).  You will get  x =  = .\r\n" );
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document.write( "       +-----------------------------------------------------+\r\n" );
document.write( "       |   So, at this point we know all the dimensions,     | \r\n" );
document.write( "       |   and now I am ready answer the questions.          |\r\n" );
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document.write( "(a)  To the nearest tenth of a centimeter, what is the length of the diagonal of the prism?\r\n" );
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document.write( "         The square of the diagonal length is  d^2 = x^2 + y^2 + z^2 =  = 38.5;\r\n" );
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document.write( "         hence, the diagonal is  d =  = 6.2 cm  (rounded).      ANSWER\r\n" );
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document.write( "(b)  What is the volume of the prism?\r\n" );
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document.write( "         The volume is  V = xyz = .. =  =  = 25.456 cm^3  (rounded).    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "All the questions are answered.\r
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\n" ); document.write( "\n" ); document.write( "You get a brilliant solution with the careful explanation.\r
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