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Math Help - optimzation problem #6

  1. #1
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    optimzation problem #6

    Find the area of the largest rectangle that can be inscribed in a right triangle with legs adjacent to the right angle of the lengths 5 cm and 12 cm. The two sides of the rectangle lie along the legs.
    Last edited by mr fantastic; August 12th 2009 at 03:45 PM. Reason: Changed post title
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  2. #2
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    Quote Originally Posted by skeske1234 View Post
    Find the area of the largest rectangle that can be inscribed in a right triangle with legs adjacent to the right angle of the lengths 5 cm and 12 cm. The two sides of the rectangle lie along the legs.
    sketch the right triangle with vertices (0,0) , (0,5) , and (12,0)

    one corner of the rectangle lies on the line between (0,5) , and (12,0).

    you need to find the equation of this line.

    area of the rectangle will be A = xy , where y is the linear equation mentioned above.

    find \frac{dA}{dx} and maximize.
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    Quote Originally Posted by skeeter View Post
    sketch the right triangle with vertices (0,0) , (0,5) , and (12,0)

    one corner of the rectangle lies on the line between (0,5) , and (12,0).

    you need to find the equation of this line.

    area of the rectangle will be A = xy , where y is the linear equation mentioned above.

    find \frac{dA}{dx} and maximize.
    Hi can you double check my equation before i proceed?

    i have

    x^2+y^2=r^2
    12^+5^2=169^2
    x^2+y^2=169^2
    y=(169^2-x^2)^0.5
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  4. #4
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    Quote Originally Posted by skeske1234 View Post
    Hi can you double check my equation before i proceed?

    i have

    x^2+y^2=r^2
    12^+5^2=169^2
    x^2+y^2=169^2
    y=(169^2-x^2)^0.5
    sorry, no Pythagoras for this problem ...

    do you understand that you're maximizing the area of a rectangle inscribed in a triangle?
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  5. #5
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    Quote Originally Posted by skeeter View Post
    sorry, no Pythagoras for this problem ...

    do you understand that you're maximizing the area of a rectangle inscribed in a triangle?
    oh.. yes.. but I am having trouble coming up with the linear equation.
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  6. #6
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    Quote Originally Posted by skeske1234 View Post
    oh.. yes.. but I am having trouble coming up with the linear equation.
    here's a picture. y = mx+b, remember?
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