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Thread: Triangle ratios

  1. #1
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    Triangle ratios

    Been playing with a geogebra file ( see below), the base of the triangle is fixed but as the point P moves along a horizontal line, the area does not change ( as height of the triangle is the same) but the lengths of the other two sides do, as we would expect.

    I wondered how the ratio of the two sides change with the x coordinate of the point P. So in the graphics 2 window I have plotted this. I have noticed a strange looking graph that seems to have a max at 3/2 and a min at 2/3 , I can't seem to get a handle of what the function might be?
    Any thoughts?

    Triangle ratios-triangle.png
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  2. #2
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    Re: Triangle ratios

    So, you are dragging the point P to the left and the right, and you want to determine the formula for the ratio AP/BP?

    Well, P has coordinates (x,3).
    $|AP| = \sqrt{(x-3)^2+36}$
    $|BP| = \sqrt{(x-8)^2+36}$

    So, your ratio has equation:

    $\dfrac{|AP|}{|BP|} = \sqrt{\dfrac{x^2-6x+45}{x^2-16x+100}}$
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