document.write( "Question 181013: If I have 100 ft. of fencing and I want to enclose the most area, should I make the enclosure a circle, triangle, or a square Prove your answer. \n" ); document.write( "

Algebra.Com's Answer #135675 by Alan3354(69443) $\"\"$ $\"About$

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If I have 100 ft. of fencing and I want to enclose the most area, should I make the enclosure a circle, triangle, or a square Prove your answer.
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\n" ); document.write( "With only 3 to choose from, it's a matter of determining area vs. perimiter.
\n" ); document.write( "Circle:
\n" ); document.write( "C = 2*pi*r = 100
\n" ); document.write( "r = 50/pi
\n" ); document.write( "Area = pi*r^2
\n" ); document.write( "Area = pi*(50/pi)^2
\n" ); document.write( "Area = 2500/pi =~795.8 sq ft
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\n" ); document.write( "Square:
\n" ); document.write( "C = 4s = 100 feet
\n" ); document.write( "s = 25 ft
\n" ); document.write( "Area = 25^2 = 625 sq ft
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\n" ); document.write( "Triangle (equilateral):
\n" ); document.write( "C = 3s = 100 feet
\n" ); document.write( "s = 100/3 feet
\n" ); document.write( "Area = bh/2
\n" ); document.write( "Area = s*(s/2)*sqrt(3)/2
\n" ); document.write( "Area = s^2*sqrt(3)/4
\n" ); document.write( "Area =~ 481 sq ft
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\n" ); document.write( "The circle encloses the greatest area.
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\n" ); document.write( "The enclosed area increases with the number of sides of the polygon, and is a maximum when the # of sides is infinite, which is a circle. \n" ); document.write( "

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