Math CentralQuandaries & Queries


If you have a scalene triangle with sides measuring 8 units, 6 units, and 10 units (and 10 is the base) how do i find the height perpendicular to the base of 10?

Hi Cassie,

I can show you three different ways to solve this problem.

  1. Use the method I used in the answer to an earlier question.

  2. Do the numbers 6, 8 and 10 mean anything special in this situation? What about half the numbers 3, 4 and 5? The triangle is a right triangle (verify using Pythagoras' theorem) and hence if the base has length 8 units then the height is 6 units and you can find its area A using half the base times the height. But you obtain the same area if the base is 10 units long and the height is the unknown h. Hence the area is 10/2 times h = A. Solve for h.

  3. The third method is similar to the second but doesn't use the fact that the triangle is a right triangle. If you know the lengths of the sides of a triangle then you can find its area A using Heron's Formula. Once you know A you can again solve for h using 10/2 times h = A.


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