SOLUTION: Please solve this question
A former has 100 sheep and every sheep needs 1m2 of field on which to graze. He wants to make a rectangular field , using the smallest amount of fencin
Question 1127946: Please solve this question
A former has 100 sheep and every sheep needs 1m2 of field on which to graze. He wants to make a rectangular field , using the smallest amount of fencing possible. What dimensions should he choose?
Regards Found 2 solutions by Alan3354, Boreal:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! Please solve this question
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A former has 100 sheep and every sheep needs 1m2 of field on which to graze. He wants to make a rectangular field , using the smallest amount of fencing possible. What dimensions should he choose?
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The smallest perimeter of a rectangle for a given area is that of a square.
You can put this solution on YOUR website! The smallest rectangle with the maximum surface area per unit perimeter is a square.
Here, he needs 100 m^2 of field.
the rectangle is x feet wide and y feet long.
the area is xy sq ft, the perimeter is 2xy
xy=100, x=100/y
perimeter is 2y+200/y
The minimum is when the derivative is 0, or when 2-200/y^2=0
2y^2=200
y^2=100
y=10, x=10
the perimeter is 40 m, and the shape is a square.
