Results 1 to 3 of 3

Math Help - Finding area of a rectangle as a function of x when...

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    6

    Finding area of a rectangle as a function of x when...

    A rectangle has a perimeter of 100 inches and one side has length x. Then, use the function found in the first part to find the dimension of the rectangle with perimeter of 100 inces and the largest possible area.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Hi

    The other side of the rectangle is 50-x
    Its area is therefore x(50-x)
    The largest area is obtained when x=25 (the rectangle is a square)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by Incursion View Post
    A rectangle has a perimeter of 100 inches and one side has length x. Then, use the function found in the first part to find the dimension of the rectangle with perimeter of 100 inces and the largest possible area.
    Hi Incursion,

    if the perimeter is 100, then half the perimeter is 50,
    which is x + other side "y", so x+y is 50, hence y=50-x

    Thus the rectangle area is xy=x(50-x) square units in terms of x.

    To find the maximum area of this rectangle,
    (since the minimum area will be zero as the opposite sides eventually touch)
    the area function is differentiated and the value of x causing it to be zero found, as the derivative gives the tangent slope,
    a tangent of slope zero balances on the maximum point of the area curve,
    which is a quadratic.

    x(x-50)=x^2-50x

    \frac{d}{dx}\left(x^2-50x\right)=2x-50

    This is zero when x=25.
    This value of x gives the rectangle of maximum area.

    y=50-x_{max}=50-25=25

    All sides are 25 inches long.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: June 2nd 2011, 04:56 PM
  2. Replies: 4
    Last Post: July 11th 2010, 11:19 PM
  3. Finding the surface area of a function
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 25th 2010, 06:12 PM
  4. Finding the area of a function and graph?
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 19th 2009, 01:23 PM
  5. Finding the rectangle of greatest area...
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 7th 2009, 05:40 PM

Search Tags


/mathhelpforum @mathhelpforum