A farmer wants to enclose a rectangular area with 120 feet of fencing. One side is a river and will not require a fence. What is the maximum area that can be enclosed?

How can I set the equation up?

Question

A farmer wants to enclose a rectangular area with 120 feet of fencing. One side is a river and will not require a fence. What is the maximum area that can be enclosed? 

How can I set the equation up?

campbell_st · Answer

well let the width by x and the length be 120 - 2x

|dw:1417370371905:dw|

the area enclosed will be

$$A = length ~~~\times~~~ width$$

or using the information in the diagram 

$$A = x \times (120 - x)$$

just distribute. 

find the 1st derivative, set it to zero and solve for x. 

find the 2nd derivative and test the solution is a maximum value. 

that will be the width, calculate the length then calculate the max area. 

hope it helps

anonymous · Answer

@campbell_st Thank you! I get it!