Maximum Area

posted by .

We have 900 ft of fencing and we want to construct a back yard. If we are using the building as part of the barrier for the yard what are the dimensions that allow maximum area?

I am not even sure how to start though I know I am supposed to calculate the derivative of the setup. Thank you

  • Maximum Area -

    if the yard has dimensions x and y, and side x is parallel to the building, then the fencing used is

    x+2y = 900
    The area is
    a = xy = (900-2y)*y = 900y - 2y^2

    da/dy = 900 - 4y
    da/dy=0 when y=900/4 = 225
    so, x = 900-2y = 450

    the yard is thus 450 by 225

  • Maximum Area -

    I do not think I made it clear sir. The part where I was stuck was where 100 ft. of the building is covered by the side of the yard.

    | yard |
    | |
    } building {

    the building length is 100 feet

    Sorry for any confusion this caused.

  • Maximum Area -

    As the text drawing did not come out clear I hope this may clarify what I meant.

    imgur /F5NJVqp

  • Maximum Area -

    You're right - you did not make it clear that the building was only 100 feet wide.

    If the building on;y covers 100 feet of the side x, then

    x+(x-100)+2y = 900
    x = 500-y

    and follow the same steps above.

    If I still have it wrong, then just draw yourself a diagram and label the various parts, making sure all the fence sections add up to 900. Then substitute for x or y in the formula a=xy.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    Chris wants to make an enclosed rectangular area for a mulch pile. She wants to make the enclosure in such a way as to use a corner of her back yard. She also wants it to be twice as long as it is wide. Since the yard is already fenced, …
  2. math

    Susan's back yard is rectangular with dimensions 39 yd. by 71 yd. Carlos's back yard is rectangular with dimensions 30 yd. by 50 yd. How much larger is the area of Susan's back yard than the area of Clarlos's back yard?
  3. Pre-Algebra-math

    Mr.jones bought 20 yards of fencing to make pen for dog pen will be in rectangle shape, the fencing comes in 1 yard section, wants the MAXIMUM areafor his dog to run, what dimension will give the pen the biggest space for dog to run?
  4. 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?
  5. Maximum Area-Calculus-Edit

    We have 900 ft of fencing and we want to construct a back yard. If we are using the building as part of the barrier for the yard what are the dimensions that allow maximum area?
  6. 5th grade math

    suppose you are building a fence for a garden in your yard. your yard is 50 ft wide and has an area of 500 square ft. your father has 88 feet of garden fencing,so your garden has to have a perimeter of 88 ft. how big an area would …
  7. calculus help

    Farmer Brown wants to fence in a rectangular plot in a large field, using a straight rock wall that is already there as the north boundary. The fencing for the east and west sides of the plot will cost $3 a yard, but she needs to use …
  8. AP Calculus

    The management of a large store has 1600 feet of fencing to fence in a rectangular storage yard using the building as one side of the yard. If the fencing is used for the remaining 3 sides, find the area of the largest yard possible.
  9. Math, Quadratic Functions

    A rectangular chicken yard was built against an existing barn wall (as shown in the picture). 30 m of fencing was used to enclose the yard. a) Find the dimensions of the yard its area is 108 m! How to solve this problem..?
  10. Algebra

    Ian wants to fence three sides of a rectangular exercise yard for his dog. The fourth side of the exercise yard will be a side of the house. He has 100 feet of fencing available. Find the dimensions that will enclose the maximum area.

More Similar Questions