Question

Ms. Jones keeps her pigs in a fenced pen that has the shape of a regular pentagon. The area of the pen is 50 ft2 and the apothem is 4 ft. Ms. Jones has decided that she wants to remake the pig living area to be in the shape of a rectangle instead. She wants to reuse the same amount of fence to make the new rectangular living space.
Ms. Jones wants to give the pigs as much living space as possible. What should the dimensions and the area of the rectangular space be in order to provide the most area with the given amount of fence? Ms. Jones plans to cut the fence only in half- and whole-foot units. Show your work and explain your reasoning.

Answer 1

First, use the formula for the area of a regular polygon that uses the apothem.
That will give you the perimeter of the regular pentagon.
Then using the perimeter, write an equation for the area of a rectangle with the same perimeter as the pentagon, and use calculus to find a maximum value.

Answer 2

whats calculus

Answer 3

@mathstudent55

Answer 4

Calculus is a type of math, just like algebra and geometry.

Answer 5

how do you find it

Answer 6

Have you fond the first part, the perimeter of the pentagon?

Answer 7

um hang on i have to eat ill be right back

Answer 8

im back

Answer 9

its 20 right as the perimeter @mathstudent55

Answer 10

can anyone heelp me

Answer 11

\(A_{polygon} = \dfrac{1}{2}ap\)

where a = apothem, and p = perimeter

Solve for p, the perimeter.