you have 600 ft of fencing to make a pen for hogs. if you have a river on one side of your property, what are the dimensions (in ft) of the rectangular pen that maximize the area?

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08-11-2022
Mathematics

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you have 600 ft of fencing to make a pen for hogs. if you have a river on one side of your property, what are the dimensions (in ft) of the rectangular pen that maximize the area?

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RK99 RK99 · Answer 1 · 2022-11-12T05:05:23-05:00

The dimensions that maximize the area are 150ft × 300ft.

What do we mean by dimensions?

A topological measurement of an object's dimension is the extent of its covering qualities.
It is, essentially, the number of coordinates required to specify a location on the object.
A cube is three-dimensional, whereas a rectangle is two-dimensional.

So, let y be the length of the side parallel to the river and x be the length of each of the two sides perpendicular to it.

The following provides the total fencing length:

2x + y = 600
y = 600 - 2x

The rectangular pen's surface area is:

A = xy
A = x(600 - 2x)
A = 600x - 2x²

We may determine the value of x required to maximize the area by determining the value of x for which the derivative of the area function is zero:

dA(x)/dx = d(600x - 2x²)/dx
0 = 600 - 4x
x = 150

The value of y is: for x=150

y = 600 - 2x = 600 - (2 × 150)
y = 300

Therefore, the dimensions that maximize the area are 150ft × 300ft.

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