Precalculus

posted by .

The owner of a horse stable wishes to set up 4 rectangular corrals of identical dimensions along the back wall of an existing barn using 200 ft of fencing. The sides of each corral will be attached to the barn, fencing is not needed along the back wall. Find the function that expresses the combined area of 4 corrals each if each corral is x feet long.

  • Precalculus -

    Did you make a sketch ?
    Even though you didn't say, I will assume that the corrals are joined with common lengths.
    let the width of the entire corral (parallel to the barn) be y ft
    let each width of corrals be x ft
    So we have y + 5x = 200
    y = 200 - 5x

    Area = xy = x(200-5x) or 200x - 5x^2

    The equation will vary depending on your definition of the variables. Mine avoids unnecessary fractions .

    BTW, after you maximize the area function, the dimensions of each corral will be 20 by 25, for a maximum area of 2000 for the combined area

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. algebra

    a rancher has 310 feet of fencing with which to enclose two rectangular corrals, both of the same size. the two corrals will share one side, and a barn forms one side of both corrals. suppose the width of each corral is X feet. express …
  2. Precalculus

    There are 4 rectangular corrals of identical dimensions along the back wall of an existing barn using 200 ft of fencing. The diagram has 4 rectangular corrals attached together but fencing is not needed on the back wall of the barn. …
  3. Precalculus

    Combined area of 1680ft^2 for 4 identical rectangular corrals. Corrals are joined together and no fencing at the back wall of the barn. 200=5d+4w 1680=4dw What length will produce the maximum area?
  4. Precalculus

    I have a diagram that has 4 rectangular corrals joined together and a barn above it. Fencing is not needed along the back wall of the barn. The perimeter is 200 ft and the question asks... If each corral is 16 ft. long (front to back) …
  5. Precalculus

    A barn has 150 feet of fencing and there are 3 rectangular corrals of identical dimensions along the back wall of the barn. The sides of each corral are attached to the barn and fencing is not needed along the back wall of the barn. …
  6. Precalculus

    A barn has 150 feet of fencing and there are 3 rectangular corrals of identical dimensions along the back wall of the barn. The sides of each corral are attached to the barn and fencing is not needed along the back wall of the barn. …
  7. Math- Please Help Us!

    Diagram has 4 rectangular corrals with a barn above it. Sides (front to back) are attached to the barn. Fencing is not needed along the back of the barn. P= 200 ft of fencing If each corral is 16 ft long (front to back), how wide will …
  8. pre calculus

    A farmer will be adding a rectangular corral to his barn. He has 600 feet of fencing. The part of the barn that is attached to the corral is 150 feet long. Write a function for the area of the corral, A(x) and include the domain Find …
  9. COLLEGE ALGREBRA

    A horse breeder wants to construct a corral next to a horse barn that is L=20 feet long, using the barn as part of one side of the corral as shown in the figure above. The breeder has 320 feet of fencing available.
  10. Geometry

    A horse breeder wants to construct a corral next to a horse barn that is L=16 feet long, using the barn as part of one side of the corral as shown in the figure above. The breeder has 280 feet of fencing available. Find the value of …

More Similar Questions