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## Homework Statement

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.

## Homework Equations

## 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.