Asked by Korir
A farmer has a 100m chainlink to fence a rectangular plot.what is the greatest area he can enclose with the chainlink
Answers
Answered by
Anonymous
a = x y
100 / 2 = x + y
so x =50-y
a = (50 -y)y = 50 y - y^2
or
y^2 - 50 y = -a
I do not know if you do calculus so will find vertex of parabola.
complete the square
y^2 - 50 y + 625 = -a + 625
(y-25)^2 = -1(a-625)
vertex at y = 25 , area = 625 so a square
======================
using calculus
a = -y^2 + 50 y
da/dy = 0 at min or max = -2 y +50
so 2 y = 50
y = 25 again
100 / 2 = x + y
so x =50-y
a = (50 -y)y = 50 y - y^2
or
y^2 - 50 y = -a
I do not know if you do calculus so will find vertex of parabola.
complete the square
y^2 - 50 y + 625 = -a + 625
(y-25)^2 = -1(a-625)
vertex at y = 25 , area = 625 so a square
======================
using calculus
a = -y^2 + 50 y
da/dy = 0 at min or max = -2 y +50
so 2 y = 50
y = 25 again
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