I'm trying to find if it is possible to find the lengths of the base and height of a right triangle with only the hypotenuse and the area (or the perimeter) of the triangle. I would have just figured that it was impossible, but I found an online calculator that could do it, but it didn't provide formulas.
[Math] Calculate sides of right triangle with hypotenuse and area or perimeter
geometrytriangles
Best Answer
From the Wikipedia article on Thales' theorem:
If you know the hypotenuse, you know the base of this diagram; if you also know the area, then you can compute the height (from $A=\frac12 bh$). Then you can draw a horizontal line at the required height; where it intersects the circle is the vertex with the right angle.