Question

rhianna wants to build a rectangular pen for some farm animals. one side of the pen will be against a barn, so no fence is needed on that side. the other three sides will require fencing. rhianna has 500 linear feet of fencing available and wants to use all of it in order to build the largest possible pen for the animals. let w be the width of the enclosure and let l be the length of the enclosure (as shown above). write an function for the area a of the enclosure in terms of w. a(w) = hint: you need find an area function in terms of w only. that means that l cannot be in your function. rhianna has 500 feet of fencing avaible. use this fact to create a fencing equation. then solve the fencing equation for l so that you have something you can use represent length in the area function.

Explanation:

Step1: Set up the fencing - length equation

The total length of the fencing is used for two widths and one length. So, $2w + l=500$.

Step2: Solve the fencing - length equation for $l$

$l = 500 - 2w$.

Step3: Write the area function

The area of a rectangle is $A=l\times w$. Substitute $l = 500 - 2w$ into the area formula: $A(w)=(500 - 2w)w=500w-2w^{2}$.

Answer:

$A(w)=500w - 2w^{2}$