A fence of length 100m is to be used to form three sides of a rectangular enclosure, the fourth side being a wall then the maximum

Question

A fence of length 100m is to be used to form three sides of a rectangular enclosure, the fourth side being a wall then the maximum area which can be enclosed by the fence is_________________​

in progress 0
Cora 3 months 2021-07-19T22:19:56+00:00 1 Answers 0 views 0

Answers ( )

    0
    2021-07-19T22:21:38+00:00

    Given : A fence of length 100m is to be used to form three sides of a rectangular enclosure,

    the fourth side being a wall  

    To Find : the maximum area which can be enclosed by the fence is

    Solution:

    Let say side opposite to wall =  2x  m

    Then sum of  remaining  two sides = 100 – 2x   m

    Length one of remaining side = (100 – 2x)/2 = 50 – x  m

    Area = (50 – x) (2x)

    =>A = 100x  – 2x²

    dA/dx  = 100 – 4x

    dA/dx  = 0

    => 100 – 4x = 0

    => x = 25

    d²A/dx²  = – 4 < 0

    Hence area is maximum when  x = 25

    Hence Area = (50 – x) (2x)

    => Area = (50 – 25) (2 * 25)

    => area = 25 * 50

    => area = 1250  m²

    maximum area which can be enclosed by the fence is  1250  m²

    Learn More:

    with rectangle of given perimeter finding the one with a maximum …

    brainly.in/question/19482093

    with rectangle of a given perimeter finding the one with a maximum …

    brainly.in/question/3878004

    . In about four (4) lines describe how to determine the area and …

    brainly.in/question/18731780

Leave an answer

Browse

9:3-3+1x3-4:2 = ? ( )