I need help on a math problem

Question

A woman wants to put some chicken-wire fencing around her strawberry patch to keep the rabbits out. She has 40 feet of fence to use.

a) Write an equation for the perimeter of the strawberry patch using x and y for the dimensions of the area. (The area will be a rectangle.)

b) Write an equation for the area, A, of the patch using x and y.

c) Use your answer from part a to eliminate y from the equation in part b, so that

A is a function only of x.

d) Find the dimensions of the patch which give a maximum value for A, and

find that maximum value.

Answer 1

a) 40 = 2x + 2y

20 = x+y

b) A=xy

c) A=x(20-x) = 20x-x^2

d)A'=20-2x=0

2x=20

x=10 feet

y=10 feet for maximum A = 100 square feet

for any perimeter, a square is the rectangle that gives maximum area

divide the perimeter by 4

40/4 = 10 x 10 feet