How do you find height knowing area and perimeter of right angle triangle?

Suppose the sides are a, b and c with c being the hypotenuse.

Then 1/2*a*b is the area which is known. Therefore b = 2*area/a

Also, by Pythagoras, c = sqrt(a2 + b2) so that, using the previous result, c can be expressed in terms of a.

So, you now have a + b + c = perimeter where both b and c can be expressed in terms of a.

This gives a quadratic equation that can be solved for a. The two solutions are a and b, since flipping the triangle will swap the base and height.