Page 2 of 2 FirstFirst 12
Results 16 to 19 of 19
Like Tree2Thanks

Math Help - Rectangle Inscribed inside a Semicircle (w/ picture)

  1. #16
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,683
    Thanks
    446

    Re: Rectangle Inscribed inside a Semicircle (w/ picture)

    Quote Originally Posted by Binary View Post
    What i can tell from what I see in my calculator. It looks like the Area = 25cm^2, But as you stated there are 4 congruent sides, so Im guessing the area = 100cm^2?
    no ... I said the rectangle's area equals 4 congruent triangle areas. The area of one triangle is \frac{1}{2} \cdot 5\cos{\theta} \cdot 5\sin{\theta}. Multiplying this expression by four gives the rectangle area, A = 25\sin(2\theta).

    Note that the maximum area of the rectangle is 25 because the largest value that \sin(2\theta) can be is 1.

    A_{max} = 25 \cdot [the \,  largest \, possible \, value \, of \, \sin(2\theta)] = 25(1) = 25
    Thanks from Binary
    Follow Math Help Forum on Facebook and Google+

  2. #17
    Newbie
    Joined
    Apr 2012
    From
    Cali
    Posts
    20

    Re: Rectangle Inscribed inside a Semicircle (w/ picture)

    So you have to look at what Max Area sin(2theta) can be? So once you have that, you substitue 1 for sin(2theta) and that equals 25cm^2, which gives you the max area of the whole rectangle?
    Follow Math Help Forum on Facebook and Google+

  3. #18
    Newbie
    Joined
    Apr 2012
    From
    Cali
    Posts
    20

    Re: Rectangle Inscribed inside a Semicircle (w/ picture)

    I see to find the Dimensions of the rectangle, I know that 2(theta)= 90 or pi/2, (theta)=45 or pi/4. How would I go about solving this part?

    -Thank you very much skeeter for all your help by the way. Your the best <3
    Last edited by Binary; April 15th 2012 at 06:36 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #19
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,683
    Thanks
    446

    Re: Rectangle Inscribed inside a Semicircle (w/ picture)

    Quote Originally Posted by Binary View Post
    I see to find the Dimensions of the rectangle, I know that 2(theta)= 90 or pi/2, (theta)=45 or pi/4. How would I go about solving this part?

    -Thank you very much skeeter for all your help by the way. Your the best <3
    you just solved it ...

    \sin(2\theta) = 1

    2\theta = \frac{\pi}{2}

    \theta = \frac{\pi}{4}
    Follow Math Help Forum on Facebook and Google+

Page 2 of 2 FirstFirst 12

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: May 20th 2009, 02:51 PM
  2. Rectangle inside semicircle
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: October 25th 2008, 05:02 PM
  3. Rectangle Inscribed in Semicircle...Part 2
    Posted in the Pre-Calculus Forum
    Replies: 8
    Last Post: September 1st 2008, 03:17 AM
  4. Rectangle Inscribed in Semicircle...Part 1
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: August 29th 2008, 06:30 PM
  5. Rectangle Inscribed in Semicircle
    Posted in the Geometry Forum
    Replies: 2
    Last Post: January 23rd 2007, 02:33 AM

Search Tags


/mathhelpforum @mathhelpforum