A farmer has 400 yards of fencing to enclose a rectangular garden. Express the area A of the rectangle as a fu

Question

A farmer has 400 yards of fencing to enclose a rectangular garden. Express the area A of the rectangle as a function of the width X of the rectangle. What is the domain of A?

Answer 1

if width = x then
length = 200 - x

400 = 2x + 2(200 -x)

and area
A = x * (200 - x) = f(x)

"domain" of f(x) = the set of all number greater than 0 and less than or equal to 100

I would NOT include 0 in the domain, since the statement said "enclose" a garden

and I used 100 instead of 200 since, by convention, length > =width

these last few points border on "quibbling"

Answer 2

the area of the rectangle is x * y
the perimeter of the rectangle is 2(x + y)= 400

to express the area in terms of x, lets convert all the y's to x's by substitution...
from perimeter ... x + y = 200 so, y = 200 -x

area = x * (200-x) = 200x - x^ .... [-x^2 + 200x]

area is the negative of x squared plus 400 times x
graphing this function yields the following ...

(-x) (x - 200) = 0 [zero's exist at x= 0, 200]
since area can't be negative, we accept the domain as (0, 200)
the maximum value of a occurs at vertex ... ( -b /2a)
(-200/ 2(-1) = 100

when x= 100, y=100 ... the area is 10,000
if x = 90 .. y= 110 ... the area is 9,900 (less than 100 x 100)

Answer 3

I'm not sure what the domain of A means but the rectangle is 20 x 20.

Answer 4

cant be 20x20 since that would be a square
length could be 40 and width could be 10
A=LxW
400=40x10

i dont have a clue what the first guy said lol

Answer 5

perimeter = 2L + 2 W
400 = 2 (L+W)
200 = L+W
200-W = L

Area = L * W
= (200-W) * W
= (200W - W)