Asked by Carolyn
Ann wants to plant a rectangular garden next to a straight river. She has 120 feet of fencing and will not fence the side of the garden next to the river. What dimensions will produce the largest garden?
Answers
Answered by
Damon
x+2y = 120
A = x y
A = (120-2y)y = 120 y - 2 y^2
2 y^2 -120 y = -A
y^2 -60 y = -A/2
y^2 - 60 y + 900 = -A/2 + 900
(y-30)^2 = -1/2(A -1800)
so y = 30
x = 120 - 60 = 60
sure enough 30*60 = 1800
A = x y
A = (120-2y)y = 120 y - 2 y^2
2 y^2 -120 y = -A
y^2 -60 y = -A/2
y^2 - 60 y + 900 = -A/2 + 900
(y-30)^2 = -1/2(A -1800)
so y = 30
x = 120 - 60 = 60
sure enough 30*60 = 1800
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