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Math Help - Find the minimum length...

  1. #1
    Newbie
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    Aug 2008
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    Find the minimum length...

    Could someone help me with this problem?

    A right triangle in the first quadrant has the coordinate axes as sides, and the hypotenuse passes through the point (1,8). Find the vertices of the triangle such that the length of the hypotenuse is minimum.


    I'm having trouble finding even the primary equation.
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  2. #2
    MHF Contributor
    Joined
    Nov 2008
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    France
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    1,458
    You can solve the problem in this way
    I call A(a,0) the point of the triangle on the x axis, B(0,b) the point on the y axis and M(1,8)
    You can find b function of a by finding the equation of (AM)
    Then you can find the length of the hypotenuse ABē function of a
    To find the minimum you just have to derivate
    After calculations I find a=5
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