Afarmer is planning a rectangular area for her chickens. the area of the rectangle will be 800 square feet. three sides of the rectangle will be formed by fencing, which costs $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 the fencing, how long should the fourth side be?

  40 ft

Step-by-step explanation:

Let x represent the length in feet of the fourth side. Then the sides perpendicular to the barn wall will have length 800/x, and the total cost of the fence will be ...

  cost = $5 × (x + 2·800/x)

The derivative of cost with respect to x will be zero when the cost is a minimum:

  d(cost)/dx = 5 -8000/x^2 = 0

  5x^2 = 8000 . . . . . multiply by x^2, add 8000

  x = √1600 =  40 . . . . feet . . . . . . divide by 5, take the square root

The length of the fourth side should be 40 feet.

40 feet.

Step-by-step explanation:

Area of rectangle =  800 square feet

Let the fourth side of the rectangle be x.

Length of the rectangle = x feet

The area of a rectangle is

Cost of fencing = $5 per foot

Cost function on three sides is

Differentiate with respect to x.

To find the critical point equate C'(x)=0.

Divide both sides by -5.

Taking square root on both sides,

Differentiate C'(x) with respect to x.

Since C''(x)>0 for x=40, therefore cost of the fencing is minimum at x=40.

Thus, the measure of fourth side of the rectangle is 40 feet.

it would not be increasing by nothing that i can see probably by 25 percent that is all i can sat\y for now if i have any thing else to say i will edit this.

step-by-step explanation:

$450 i think. hope this ☺