Results 1 to 2 of 2

Math Help - this is applied maximum and minimum problems

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    16

    this is applied maximum and minimum problems

    a rectangle is to be inscribed in a right triangle having sides of lengty 6 in, 8 in, and 10 in. find the dimension of the rectangle with greatest area..
    tq~
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by redcherry View Post
    a rectangle is to be inscribed in a right triangle having sides of lengty 6 in, 8 in, and 10 in. find the dimension of the rectangle with greatest area..
    tq~
    Hi redcherry,

    If you draw the right-triangle, with an arbitrary inscribed rectangle,
    that has sides against the base and vertical side, settling in the
    right-angled corner.

    label the base of the triangle 6, height 8, hypotenuse 10.

    The rectangle base is x and the rectangle height y.

    Now, observe the smaller identical triangle at the bottom corner.
    It has base (6-x) and height y.

    Hence we can write an equation

    tan\theta=\frac{y}{6-x}=\frac{8}{6}\ \Rightarrow\ 6y=8(6-x)\ \Rightarrow\ y=\frac{8}{6}(6-x)

    Rectangle area is

    xy=\frac{8x}{6}(6-x)

    in terms of x only, allowing us to differentiate the area and equate the derivative to zero to find the rectangle of maximum area

    \frac{8}{6}\frac{d}{dx}\left[x(6-x)\right]=\frac{8}{6}\frac{d}{dx}\left(6x-x^2\right)

    =\frac{8}{6}(6-2x)

    which equals zero when x=3

    x=3,\ y=\frac{8}{6}(6-3)=4
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. this is applied maximum and minimum problems
    Posted in the Calculus Forum
    Replies: 0
    Last Post: March 2nd 2010, 01:29 AM
  2. this is applied maximum and minimum problems
    Posted in the Calculus Forum
    Replies: 0
    Last Post: March 2nd 2010, 01:22 AM
  3. applied maximum and minimum problem #2
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 28th 2010, 11:13 AM
  4. Replies: 1
    Last Post: February 28th 2010, 11:10 AM
  5. applied maximum and minimum problem #3
    Posted in the Calculus Forum
    Replies: 0
    Last Post: February 28th 2010, 08:06 AM

Search Tags


/mathhelpforum @mathhelpforum