SOLUTION: A retangular field is to be enclosed by 500m of fence. What dimensions will give the maximum area? What is the maximum area? Solution: Let the length of rectangle = x So the wid

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: A retangular field is to be enclosed by 500m of fence. What dimensions will give the maximum area? What is the maximum area? Solution: Let the length of rectangle = x So the wid      Log On


   

Question 196949: A retangular field is to be enclosed by 500m of fence. What dimensions will give the maximum area? What is the maximum area?
Solution:
Let the length of rectangle = x
So the width will be, w
perimeter = 2%28x%2Bw%29=500
or x+w=250
or w=250-x

So the area,A(x) = x%28250-x%29
A(x)=-x%5E2%2B250x
Area is maximum at the vertex if the parabola
made by the equation, A(x)=-x%5E2%2B250x
vertex=[(-b/2a),A(-b/2a)]
-b/2a = -250%2F%282%2A-1%29 = 125
A(250) = -%28125%5E2%29%2B%28250%2A125%29 = 15625
So Length,x =125m
Width = 250-125 = 125m
Maximum area = 15625m%5E2
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