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Math Help - Rectangle is Inscribed (Did I do it right?)

  1. #1
    Junior Member asemh's Avatar
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    Rectangle is Inscribed (Did I do it right?)

    Hi I am working on this Optimization Question but like usual, I am never sure if I am doing it right.

    The question is:
    A rectangle is inscribed in a semi circle of radius 25cm. Find the largest area of such a rectangle.

    Here is what i have done so far:


    Can someone tell me what steps I have done wrong? And what should I do next?

    Thanks
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  2. #2
    Super Member
    earboth's Avatar
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    Quote Originally Posted by asemh View Post
    Hi I am working on this Optimization Question but like usual, I am never sure if I am doing it right.

    The question is:
    A rectangle is inscribed in a semi circle of radius 25cm. Find the largest area of such a rectangle.

    Here is what i have done so far:


    Can someone tell me what steps I have done wrong? And what should I do next?

    Thanks
    1. The labeling in the drawing should have 2x as length of the rectangle. The 2nd line should read: x^2+y^2=25^2

    2. All calculations are OK. Calculate now y and A.
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  3. #3
    Junior Member asemh's Avatar
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    To find y,

    I plugged my x into y = sqrt(625 - x^2) and got 17.68
    when i plugged it into my area formula i got 625

    Would that be the correct answer?
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  4. #4
    Super Member
    earboth's Avatar
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    Quote Originally Posted by asemh View Post
    To find y,

    I plugged my x into y = sqrt(625 - x^2) and got 17.68
    when i plugged it into my area formula i got 625

    Would that be the correct answer?
    Yes
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