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Math Help - help please optimization!

  1. #1
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    help please optimization!

    Find the maximal area of a rectangle inscribed in a right triangle whose two lengs have length 6 and 8

    Help!
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  2. #2
    Newbie drop10's Avatar
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    Given: Need to find the maximum area of a rectangle inscribed in a right-triangle with legs with lengths 6 and 8 respectively.

    Solution:
    Find an equation for the boundary lines:
    <br />
x=0<br />
    <br />
y=0<br />
    <br />
y=8-\frac{4}{3}x<br />

    Now, find the equation of the area of the circle:
    <br />
Area(x,y) = x*y<br />
    <br />
Area(x) = x*(8-\frac{4}{3}x)<br />
    <br />
Area(x) = 8x - \frac{4}{3}x^2<br />
    Now find the vertex \frac{-b}{2a} = \frac{-8}{2*(\frac{-4}{3})} = \frac{4}{\frac{4}{3}} = 3
    Substitute x=3 into the equation for area to get your answer (I'll let you do it yourself )
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  3. #3
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    Ok but any tips on how to do it with calculus?
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  4. #4
    Newbie drop10's Avatar
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    Yea, sure!
    Instead of finding the vertex using \frac{-b}{2a},take the derivative and find where it is zero and you will get the same answer.
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  5. #5
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    mr fantastic's Avatar
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    Quote Originally Posted by amma0913 View Post
    Ok but any tips on how to do it with calculus?
    You were given the rule for area as a function of x - the hard part of the question. If you're attempting questions like this then you should already know how to use calculus to find the maximum of a function.
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