document.write( "Question 949978: Is it possible to have a rectangular playground area made from 70 yards of fencing with an area of 324 square yards? Explain with calculations. \n" ); document.write( "
Algebra.Com's Answer #580015 by rothauserc(4718)\"\" \"About 
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Perimeter(P) = 2*length(l) + 2*width(w) and
\n" ); document.write( "Area(A) = l*w
\n" ); document.write( "we are given
\n" ); document.write( "2*l +2*w = 70 and
\n" ); document.write( "l*w = 324
\n" ); document.write( "solve first equation for l and subsitute in second equation for l
\n" ); document.write( "2l = 70 -2w
\n" ); document.write( "l = 35 -w
\n" ); document.write( "2*(35-w) *w = 324
\n" ); document.write( "(70-2w)*w = 324
\n" ); document.write( "-2w^2 +70w -324 = 0
\n" ); document.write( "divide both sides of = by -2
\n" ); document.write( "w^2 -35w +162 = 0
\n" ); document.write( "using quadratic formula to solve we have
\n" ); document.write( "w = (35+24.020824299) / 2 = 29.510412149 is approx 29.5 yards
\n" ); document.write( "w = (35-24.020824299) / 2 = 5.489587851 is approx 5.5 yards
\n" ); document.write( "we have two cases, width is either 29.5 yards or 5.5 yards
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\n" ); document.write( "if width is 29.5, then
\n" ); document.write( "2*l + 2*29.5 = 70
\n" ); document.write( "2l + 59 = 70
\n" ); document.write( "2l = 11
\n" ); document.write( "l = 5.5 and
\n" ); document.write( "5.5 * 29.5 = 324
\n" ); document.write( "162.25 does not equal 324
\n" ); document.write( "**********
\n" ); document.write( "if width is 5.5, then length is 29.5 and
\n" ); document.write( "29.5 * 5.5 = 324
\n" ); document.write( "162.25 does not equal 324
\n" ); document.write( "**********
\n" ); document.write( "It is not possible to build this rectangular playground area\r
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