A rancher with 750 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. Find a function that models the total area of the four pens.

Using the area and perimeter of triangle formula, the function which models the total area of the four pens is A(L) = 0.4L² + 75L

Recall :

Dividing the pens into 4 whuvhbarw parallel means the The perimeter of of the fence can be defined thus :

5 widths and 2 lengths

Perimeter = 2(L + W)

750 = 2(2L + 5W)

750 = 4L + 10W

We can solve for Width, W ;

10W = 750 - 4L

Divide both sides by 10

W = 75 - 0.4L

Recall ;

Area of rectangle = Length × width = L × W

Substitute, W = 75 - 0.4L into the area Formula ;

A(L) = L × (75 - 0.4L)

A(L) = 75L - 0.4L²

A(L) = 0.4L² + 75L

Therefore, the function which models the total area of the four pens is A(L) = 0.4L² + 75L

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Let W represent width of rectangle and L represent length pf rectangle.

We have been given that a rancher with 750 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle.

First of all, we need to draw a diagram using our given information as shown in the attachment.

We can see that the total fencing will be equal to perimeter of four pens.

Now we will equate total fencing with perimeter as:

Let us solve for L.

We know that the area of rectangle is length times width.

Upon substituting value of L in area equation, we will get:

Therefore, our required function would be .

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