Ask questions and get helpful answers.
Ask a New Question
  1. Questions
  2. Algebra and Trig

Aldo has feet of fencing. He will use it to form three sides of a rectangular garden. The fourth side will be along a house and will not need fencing. What is the maximum area that the garden can have?

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
April
2 answers

  1. missing info
    how many feet of fencing?

    Suppose he has 120 feet, change the solution below to the appropriate number of feet in your question

    let length of field be y, (y being parallel to house.)
    let the width be x

    2x + y = 120
    y = 120-2x

    area = xy
    = x(120-2x)
    = 120x - 2x^2

    If you are in Calculus .....
    d(area)/dx = 120 - 4x = 0 for a max area
    x = 30
    y = 120-2(30) = 60
    Max area = 30(60) = 1800 ft^2

    if you don't take Calculus, complete the square
    area = -2(x^2 - 60x + 900 - 900 )
    = -2(x-30)^2 + 1800

    max area is 1800, when x = 30

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
    Reiny

  2. Considering all rectangles with a given perimeter, one side being another straight boundry, the 3 sided
    rectangle enclosing the greatest area has a length to width ratio of 2:1.

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
    tchrwill

Answer this Question

Related Questions

  1. math

    A rectangular lot is bordered on one side by a stream and on the other 3 sides by 600m of fencing. The area is a maximum. Determine the area.

  2. calculus

    using the two existing corner sides of an existing wall, what is the maximum rectangular area that can be fenced by a fencing material 30 ft long?

  3. algebra 1

    A rectangular field is enclosed by 360 feet of fencing. What is the length, in feet, of the field if its length is 6 feet more than its width?

  4. Math Calculus

    Three sides of a fence and an existing wall form a rectangular enclosure. The total length of a fence used for the three sides is 240 ft. Let x be the length of two sides perpendicular to the wall as shown. Write an equation of area A of the enclosure as a

  5. Calculus

    A farmer wants to fence a rectangular area of 800,000 m² and divide it in half with a fence that is parallel to one of the sides of the rectangle, and twice as expensive as the fence on the outer sides. How can this be done in order to minimize the cost

  6. math

    a farmer has 360 feet of fencing to make three identical adjacent rectangular pens. What dimensions of each pen will maximize the total enclosed area?

  7. algebra

    Daisy is building a rectangular pen for her chickens along one wall in her back yard. She needs to build a fence along the remaining three sides of the pen. She represents this situation with the inequality w+2ℓ≤125. Which explanation correctly

  8. Math please help

    A farmer has 120 feet of fencing available to build a rectangular pen for her pygmy goats. She wants to give them as much room as possible to run. What are the dimensions of the rectangular pen with the largest area?

  9. diff calculus

    1.) triangular corner lot has perpendicular sides of lengths 120 feet and 160 feet. Find the dimensions of the largest rectangular building that can be constructed on the lot with sides parallel to the streets.

  10. MATH

    Elaine is painting a fence. She knows that she needs 1 gallon of paint for each 10 feet of fencing. The fencing will enclose a rectangular yard that is 3 yards long and 2 yards wide. How much paint does Elaine need? (Remember 3 feet = 1 yard)

Still need help?

You can ask a new question or browse existing questions.