SOLUTION: Maximum and minimum word problem assignment 3. A rectangualr field is to be enclosed by 500m of fence. What dimensions will give the maximum area? What is the maximum area? do i

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Question 175756: Maximum and minimum word problem assignment
3. A rectangualr field is to be enclosed by 500m of fence. What dimensions will give the maximum area? What is the maximum area?
do it faster please and send it to me faster ok thanks alot
Answer by PTER(3) About Me  (Show Source):
You can put this solution on YOUR website!
x = length, y = width, A = area
2x + 2y = 500 isolate one variable
y = 250 - x
 
Substitude y = 250 - x.
A = xy
A = x(250 - x)
= -x^2 + 250x
 
Complete the square.
-x^2 + 250x = - (x^2 - 250x)
= - (x^2 - 250x + 15625) + 15625
= - (x - 125)^2 + 15625
 
Maximum 15625 at x = 125
 
A square will always give you the maximum area. The maximum area is 15625m^2. The dimensions are 125m by 125m.
 
Knowing that a square will always give you the maximum area,
 
500 / 4 = l or w
l^2 or w^2 = maximum area.