David has 1600 yards of fencing and wishes to enclose a rectangle area

Question

Express the area A of the rectangle as a function of the width W of the rectangle 

For what value of W is the area largest

What is the maximum area 

Answer 1

the largest area is always a square

1600/4=400

400 yds by 400 yds

A=400*400

A=160,000 square yards is the maximum area

using algebra...

P=2l+2w

1600=2l+2w

800=l+w

l=800-w

A=l*w

A=(800-w)*w

A=800w-w^2

y=800w-w^2

this is a parabola that opens downward so it has a maximum point

the vertex of the parabola is (h,k) 

h=-b/2a

h=-800/(2*[-1])

h=-800/-2

h=400 (w=400)

replace each w with 400 in y=800w-w^2

k=800*400-400^2

k=320,000-160,000

k=160,000 square yards is the maximum area again