Question 1127946
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.