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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.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! Perimeter(P) = 2*length(l) + 2*width(w) and
Area(A) = l*w
we are given
2*l +2*w = 70 and
l*w = 324
solve first equation for l and subsitute in second equation for l
2l = 70 -2w
l = 35 -w
2*(35-w) *w = 324
(70-2w)*w = 324
-2w^2 +70w -324 = 0
divide both sides of = by -2
w^2 -35w +162 = 0
using quadratic formula to solve we have
w = (35+24.020824299) / 2 = 29.510412149 is approx 29.5 yards
w = (35-24.020824299) / 2 = 5.489587851 is approx 5.5 yards
we have two cases, width is either 29.5 yards or 5.5 yards
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if width is 29.5, then
2*l + 2*29.5 = 70
2l + 59 = 70
2l = 11
l = 5.5 and
5.5 * 29.5 = 324
162.25 does not equal 324
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if width is 5.5, then length is 29.5 and
29.5 * 5.5 = 324
162.25 does not equal 324
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It is not possible to build this rectangular playground area
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