Problem: Comparison of altitude and median in a right triangle
Take a right triangle and let its altitude from the right angle divide the hypotenuse into parts of lengths a and b. Interpret the comparison of the lengths of the altitude and the median from the 90 degree vertex of a right triangle having hypotenuse of length a+b.

Clearly, the length of the median is always greater than or equal to the length of the altitude. Express the lengths of median and the altitude in terms of a and b.

Conclusion? _______________________________

Hints/Solution:

  • See Arithmetic Mean -- Geometric Mean Inequality


    • Comments:


    Extensions/Variations:

    Consider the triangles inscribed in a semicircle with one side formed by the diameter.

     



    Reference:

    Back to the EMAT 6600 Page.