Results 1 to 6 of 6

Math Help - figuring out height/width from area

  1. #1
    Newbie
    Joined
    Jun 2011
    Posts
    3

    figuring out height/width from area

    hello everyone
    i have a rectangle that is 14*18
    which is 252 sq. in.

    i need to get the H&W of a rectangle that its area is some percent of 252 (lets say half)
    so what will the H&W be for 126 sq.in. if it would have the same ratio as 14*18?

    thank you very much

    i need the formula, not the answer for this specific example
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123

    Re: figuring out height/width from area

    Quote Originally Posted by yisman View Post
    hello everyone
    i have a rectangle that is 14*18
    which is 252 sq. in.

    i need to get the H&W of a rectangle that its area is some percent of 252 (lets say half)
    so what will the H&W be for 126 sq.in. if it would have the same ratio as 14*18?

    thank you very much

    i need the formula, not the answer for this specific example
    1. Let H, W denote the original height and width of the rectangle and h, w the height and width of the transformed rectangle. Then you know

    \dfrac hH = k~\implies~h = k \cdot H

    \dfrac wW = k~\implies~w = k \cdot W

    2. The area of the original rectangle is: A_o = H \cdot W

    and the area of the transformed rectangle is:
    A_t = h \cdot w = (k \cdot H) \cdot (k \cdot W) = k^2 \cdot A_o~\implies~k=\sqrt{\dfrac{A_t}{A_o}}

    3. With your example:
    A_o = 252
    A_t = 126
    Plug in into the equation above:

    126 = k^2 \cdot 252~\implies~k^2=\frac12~\implies~k=\frac12 \cdot \sqrt{2}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2011
    Posts
    3

    Re: figuring out height/width from area

    thanks
    it was that sqr root that i needed!
    where do i "mark as answer"?
    thanks again
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,082
    Thanks
    66

    Re: figuring out height/width from area

    So really, you need a formula for side lengths of a given ratio; also given is area.
    a = area (126 in your example), ratio = u/v (14/16 = 7/9 in your example).
    x,y = side lengths

    General case formula: x = SQRT(au / v) ; y = a / x

    With your example:
    x = SQRT(126*7/9) = 7SQRT(2)
    y = 126 / 7SQRT(2) = 9SQRT(2)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jun 2011
    Posts
    3

    Re: figuring out height/width from area

    thanks
    ur formula is better, as i needed it for a program script, which doesnt realy accept latex... :-)
    thnak you
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,082
    Thanks
    66

    Re: figuring out height/width from area

    Quote Originally Posted by yisman View Post
    ur formula is better, ......
    For your benefit: use "your", NOT "ur".
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Area as a function of width
    Posted in the Algebra Forum
    Replies: 8
    Last Post: September 25th 2011, 02:57 PM
  2. express the area A as a function of the width X
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: June 27th 2011, 10:52 PM
  3. Expressing Area in terms of Width
    Posted in the Geometry Forum
    Replies: 8
    Last Post: November 3rd 2009, 07:47 PM
  4. Width and Height of Solid
    Posted in the Geometry Forum
    Replies: 2
    Last Post: December 9th 2008, 08:51 PM
  5. Replies: 2
    Last Post: October 20th 2008, 03:32 AM

Search Tags


/mathhelpforum @mathhelpforum