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Thread: Rectangle inscribed in semicircle, find perimeter and more

  1. #1
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    Rectangle inscribed in semicircle, find perimeter and more

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    A rectangle is inscribed in a semicircle and the radius is 1. The bas of the rectangle is x. Write an expression for the rectangle perimeter and determine the value of x that gives the highest possible perimeter. Also, what is the highest perimeter?

    Well... I fooled around with the unit circle, but still no progress. I've found several instructions on how to find the area, but no luck with perimeter.

    I'm actually desperate enough to actually pay for a solution, ben stuck on this problem for days now.
    Could any kind soul help me out?

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  2. #2
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    Re: Rectangle inscribed in semicircle, find perimeter and more

    I'm actually desperate enough to actually pay for a solution ...
    This is not a pay site, so don't offer.

    See the attached diagram ...

    $P = 2\left(x+\sqrt{1-\dfrac{x^2}{4}}\right)$

    $A = x\sqrt{1-\dfrac{x^2}{4}}$

    What method(s) have you learned for optimizing the perimeter and area? Graphing calculator solution? Calculus solution?
    Attached Thumbnails Attached Thumbnails Rectangle inscribed in semicircle, find perimeter and more-inscribed_rectangle.png  
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  3. #3
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    Re: Rectangle inscribed in semicircle, find perimeter and more

    Quote Originally Posted by skeeter View Post
    This is not a pay site, so don't offer.

    See the attached diagram ...

    $P = 2\left(x+\sqrt{1-\dfrac{x^2}{4}}\right)$

    $A = x\sqrt{1-\dfrac{x^2}{4}}$

    What method(s) have you learned for optimizing the perimeter and area? Graphing calculator solution? Calculus solution?
    >Calculus solution

    Thank you for your reply
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