The altitude perpendicular to the hypotenuse of a right triangle is 12 cm. Express the length of the hypotenuse as a function of the perimeter.
The Attempt at a Solution
So I have to express the hypotenuse (h) in terms of the perimeter. I tried to find the area of the triangle using two different equations
1) A = (1/2)*12*h = 6h
2) A = (1/2)*xy, let x and y be the other sides of the triangle
I can set them to each other, but I get 6h = 0.5xy
The perimeter (P) is x+y+h.
I have no idea how to express h in terms of P since now I have too many variables.
I tried substitution, and the best I got (without using x and y) was some complicated polynomial with P and h that I couldn't just simply solve for h.
Any tips are appreciated.