Algebra

A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 440 feet of fencing is used. Find the dimensions of the playground that maximize the total enclosed area. Remember to reduce any fractions and simplify your answers as much as possible.

-What is the shorter side of the playground? (220/3 sq ft)
-What is the longer side of the playground?
-What is the maximum area?

I know the shorter side is 220/3 sq ft, but I'm having difficulty getting the next two answers.

  1. 👍 0
  2. 👎 0
  3. 👁 1,559
  1. I will assume you made a diagram.
    On my diagram, I have each of the long sides as y, and each of the 3 shorter sides as x
    so we have 3x + 2y = 440
    y = (440 - 3x)/2 = 220 - (3/2)x

    area = xy
    = x(220 - (3/2)x)
    = 220x - (3/2)x^2

    from the subject title, I assume you don't take Calculus, then this would be easy from here on, so ....

    area = 220x - (3/2)x^2 is a downwards opening parabola, thus the area will have a maximum

    we need the vertex.
    Easiest way to get the vertex,
    the x of the vertex is -b/(2a)
    = -220/-3
    = 220/3 , which you had but it should be ft, not square feet

    so if x = 220/3
    y = 220 - (3/2)(220/3)
    = 220 - 110
    = 110

    short side is 220/3 ft, longer side is 110 ft
    area = xy
    = (220/3)(110)
    = 24200/3 or 8066 2/3 square feet
    or appr 8066.7 ft^2

    1. 👍 0
    2. 👎 0
  2. No, not in calculus yet - I will take that next.

    Thank you so much for your help!

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus 1 optimization

    A farmer wants to fence an area of 6 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What should the lengths of the sides of the rectangular field

  2. Math

    1. A gardener has 140 feet of fencing to fence in a rectangular vegetable garden. Find the dimensions of the largest area he can fence. Find the possible rectangular area he can enclose. 2. Suppose a farmer has a large piece of

  3. Calculus

    A rectangular field is to be enclosed by a fence and divided into three lots by fences parallel to one of the sides. Find the dimensions of the largest field that can be enclosed with 800 feet of fencing. Help me please!!!!!!!!!!!

  4. Algebra

    To make an enclosure for chickens, a rectangular area will be fenced next to a house. Only 3 sides will need to be fenced. There is 120 ft. of fencing material. a. What quadratic function represents the area of the rectangular

  1. math

    A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Five hundred and forty feet of fencing is used. Find the dimensions of the playground that maximize the total

  2. AP Calculus AB

    The fence around Wayne Manor (a rectangular plot of land) is going to be replaced. No fence will be required for the side lying along Gotham river. If the new wrought iron fence costs $12 per meter for the side parallel to the

  3. Math

    A farmer wants to fence in an area of 15000 m² in a rectangular field and then divide it into half with a fence parallel to one sides of the rectangle. How can he do this so as to minimize the cost of the fence?

  4. Math

    A farmer wishes to put a fence around a rectangular field and then divide the field into three rectangular plots by placing two fences parallel to one of the sides. If the farmer can afford only 1600 yards of fencing, what

  1. math

    The owner of a garden supply store wants to construct a fence to enclose a rectangular outdoor storage area adjacent to the store, using part of the side of the store (which is 260 feet long) for part of one of the sides. (See the

  2. Calculus

    ABC Daycare wants to build a fence to enclose a rectangular playground. The area of the playground is 900 square feet. The fence along three of the sides costs $5 per foot and the fence along the fourth side, which will be made of

  3. Quadratic Equations, math

    A rectangular feel measures 15m by 20m. A rectangular area is to be fenced in by reducing each dimension by the same amount. The fenced in area will be 1/2 the original area. What will the dimensions of the fenced in area be? I'm

  4. Calculus

    A rancher wants to fence in an area of 500000 square feet in a rectangular field and then divide it in half with a fence down the middle, parallel to one side. What is the shortest length of fence that the rancher can use?

You can view more similar questions or ask a new question.