document.write( "Question 1137043: Find the dimensions of the box described.
\n" ); document.write( "The length is 5 inches more than the width. The width is 4 inches more than the height. The volume is 416 cubic inches. Find the length, width, and height. \n" ); document.write( "

Algebra.Com's Answer #754877 by ikleyn(52866) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Let w be the width.\r\n" );
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document.write( "Then the length is (w+5) and the height is (w-4).\r\n" );
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document.write( "The equation for the volume is\r\n" );
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document.write( "    w*(w+5)*(w-4) = 416.\r\n" );
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document.write( "Notice that  416 = 8*13*4 - I decomposed the number 416 into the product of 3 factors.\r\n" );
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document.write( "It can be done by different ways, but I took the care that the second factor is 5 more than the first and the third is 4 less than the first -\r\n" );
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document.write( "exactly as the numbers w, (w+5) and (w-4) in the left side of equation (1).\r\n" );
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document.write( "It gives me a confidence that I correctly guessed the solution.\r\n" );
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document.write( "The plot below shows that the guessed solution w = 8 is UNIQUE.\r\n" );
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document.write( "    \r\n" );
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document.write( "    Plot y = x*(x+5)*(x-4) (red) and y = 416 (green)\r\n" );
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document.write( "ANSWER.  The width is 8 inches;  the length is  8+5 = 13 inches;  the height is  8-4 = 4 inches.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Probably, there are other ways to find the solution algebraically on more strict base, but what is done is enough to me . . . \r
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