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Sagot :
Therefore, L has a relative and absolute minimum when x = 400 m
What is Perimeter and Area ?
The area is as defined as the amount of space occupied by any shape in two dimensions. Whereas, Perimeter is the boundary or the outline of a flat shape.
Let x = length of the side parallel to the river
y = length of each of the other two sides
Then xy = 80,000, so y = 80,000/x
Minimize: L = length of the fence
L = x + 2y
= x + 160,000/x, where x > 0
L' = 1 - 160,000/x2 = (x2 - 160,000)/x2
L' = 0 when x = 400 or -400
Since x can't be negative, x must be 400.
When 0 < x < 400, L' < 0. So, L is decreasing.
When x > 400, L' > 0. So L is increasing.
Therefore, L has a relative and absolute minimum when x = 400 m
y = 80,000/x = 200 m
The fence is shortest if the side parallel to the river has length 400 m and the other 2 sides each have length 200 m.
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