document.write( "Question 574350: Mike has 24 feet of fencing. He wants to enclose the greatest area he can. Which shape would Mike use?
\n" ); document.write( "9x3
\n" ); document.write( "10x2
\n" ); document.write( "6x6
\n" ); document.write( "12 x 4
\n" ); document.write( "How do we solve this problem? \n" ); document.write( "

Algebra.Com's Answer #369074 by KMST(5328) $\"\"$ $\"About$

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With the choices, this is not a very difficult problem.
\n" ); document.write( "If the fenced area has to be a rectangle, we want the perimeter to be 24 feet because to get the largest fenced area we want to use all the fencing available.
\n" ); document.write( "Half of the perimeter (12 feet) would be the sum of the lengths of two adjacent sides (maybe a long side plus a short side).
\n" ); document.write( "For a rectangle 12 feet long by 4 feet wide we would need
\n" ); document.write( "2(12+4) = 32 feet of fencing, so the last option does not work, because we do not have enough fencing.
\n" ); document.write( "The first three choices could be used. We have enough fencing, because
\n" ); document.write( "9+3=12
\n" ); document.write( "10+2=12 and
\n" ); document.write( "6+6=12
\n" ); document.write( "The question is which would give you the largest area.
\n" ); document.write( "Area is calculated as length times width, so the areas of those three rectangles, in square feet would be
\n" ); document.write( " $\"9%2A3=27\"$
\n" ); document.write( " $\"10%2A2=20\"$ and
\n" ); document.write( " $\"6%2A6=36\"$
\n" ); document.write( "So, a square, 6 feet by 6 feet, is the best of the choices given, the one with the greatest area.
\n" ); document.write( "Without the choices, this is a quadratic function/parabola problem, and that's pretty advanced algebra.
\n" ); document.write( "Assuming that it has to be a rectangle, we would call the lengths of the sides $\"x\"$ and $\"y\"$ , and would say that
\n" ); document.write( " $\"x%2By=12\"$ --> $\"y=12-x\"$ , and the area would be
\n" ); document.write( " $\"Area=x%2Ay=x%2812-x%29=-x%5E2%2B12x\"$
\n" ); document.write( "So the area ys a quadratic function of x, which would graph as a parabola.
\n" ); document.write( "The maximum is at
\n" ); document.write( " $\"x=-12%2F%282%2A%28-1%29%29=6\"$ , so $\"highlight%28x=6%29\"$ . Then, $\"highlight%28y=6%29\"$ too, because $\"y=12-6=6\"$ \n" ); document.write( "

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