Ask Question
21 June, 15:40

Ramon wants to fence in a rectangular portion of his back yard against the back of his garage for a vegetable garden. he plans to use 40 feet of fence, and needs fence on only three sides. find the maximum area he can enclose. (hint: the lengths of the 3 fenced sides of the rectangle must add up to 40.)

+4
Answers (1)
  1. 21 June, 15:53
    0
    The first thing to do is find the perimeter of the fence:

    l + 2w = 40,

    l = length

    w = width

    By definition the area of a rectangle is:

    A = l * w

    Clearing the perimeter found:

    l = 40-2w

    We substitute l in the expression of the area:

    A = w * (40-2w)

    We rewrite:

    A = - 2w ^ 2 + 40w

    We observe that it is a parabola that opens downwards

    We find the maximum of the function:

    A ' = - 4w + 40 = 0

    4w = 40

    w = 10

    Substituting in the expression of length:

    l = 40-2 (10) = 20

    The maximum area is then:

    A = (10) * (20) = 200 feet ^ 2

    Answer:

    the maximum area he can enclose is 200 feet ^ 2
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “Ramon wants to fence in a rectangular portion of his back yard against the back of his garage for a vegetable garden. he plans to use 40 ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers