document.write( "Question 1207290: A veterinarian wishes to use 168 feet of chain-link fencing to enclose a rectangular region and subdivide the region into two smaller rectangular regions, as shown in the following figure. If the total enclosed area is 1026 square feet, find the width w and length l of the enclosed region.
\n" ); document.write( "w = ft (smaller width) by l = ft
\n" ); document.write( "w = ft (larger width) by l = ft \n" ); document.write( "

Algebra.Com's Answer #845075 by Theo(13342) $\"\"$ $\"About$

You can put this solution on YOUR website!
as far as i can tell, the enclosed region has 2 lengths and 3 widths.
\n" ); document.write( "2 lengths and 2 widths are on the outside of the enclosed region.
\n" ); document.write( "one width splits the enclosed region into two smaller regions that are equal in area.\r
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\n" ); document.write( "\n" ); document.write( "i get the following two possibilities.\r
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\n" ); document.write( "\n" ); document.write( "the length is 27 and the width is 38.
\n" ); document.write( "the length is 18 and the width if 57.\r
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\n" ); document.write( "\n" ); document.write( "length * width = 1026 in both cases.
\n" ); document.write( "2 lengths and 3 widths = 168 in both cases.\r
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\n" ); document.write( "\n" ); document.write( "my equations were:\r
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\n" ); document.write( "\n" ); document.write( "length * width = 1026
\n" ); document.write( "2 * length + 3 * width = 168.\r
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\n" ); document.write( "\n" ); document.write( "i solved for length * width from length * width = 1026.
\n" ); document.write( "this led to length = width / 1026.\r
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\n" ); document.write( "\n" ); document.write( "i substituted for length in 2 * length + 3 * width = 168 to get:
\n" ); document.write( "2 * 1026 / width + 3 * width = 168.\r
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\n" ); document.write( "\n" ); document.write( "i multiplied both sides of taht equation by width to get:
\n" ); document.write( "2 * 1026 + 3 * width squared = 168 * width.\r
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\n" ); document.write( "\n" ); document.write( "i subtracted 168 * width from both sides of the equation to get:
\n" ); document.write( "2 * 1026 + 3 * width squared - 168 * width = 0
\n" ); document.write( "i simplified and order in descending order of degree to get:
\n" ); document.write( "3 * width squared - 168 * width + 2052 = 0\r
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\n" ); document.write( "\n" ); document.write( "i factored this quadratic equation to get width = 38 or 18.\r
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\n" ); document.write( "\n" ); document.write( "when width was 38, length was 27.
\n" ); document.write( "when width was 18, length was 57.\r
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\n" ); document.write( "\n" ); document.write( "length * width = 1026 in both equations.
\n" ); document.write( "2 * length + 3 * width = 168 in both equtions.\r
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\n" ); document.write( "\n" ); document.write( "those appeared to be two feasible solutions to the problem as i understood it.
\n" ); document.write( "my diagram looked like this:\r
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