Afarmer is planning a rectangular area for her chickens. the area of the rectangle will be 200 square feet. three sides of the rectangle will be formed by fencing, which cost 5$ per foot, the fourth side of the rectangle will be formed by a portion of the barn wall, which requires no fencing. in order to minimize the cost of fencing, how long should the fourth wall be?

Let

x---------> the length side of the rectangular area

y---------> the width side of the rectangular area

we know that

the area of the rectangle is equal to

-----> equation

The perimeter of the rectangle is equal to

but remember that the fourth side of the rectangle will be formed by a portion of the barn wall

so

-----> equation

To minimize the cost we must minimize the perimeter

Substitute the equation in the equation

Using a graph tool

see the attached figure

The minimum of the graph is the point

that means for

the perimeter is a minimum and equal to

Find the value of y

The cost of fencing is equal to

therefore

the answer is

the length side of the the fourth wall will be

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нσρє ι ¢συℓ∂ нєℓρ уσυ.