I can't seem to figure ou the following problem:
A right triangle has sides $x$, $y$ and $z$, where $x$ is the hypotenuse.
$$x + y + z = 6$$
Determine the expression of the function $A(x)$ that gives the area of the triangle as a function of $x$.
The answer is $A(x) = 9 - 3x$ but I need to demonstrate the solution.
we have $$A=\frac{yz}{2}$$ from the condition we get $$y^2+z^2+2yz=36+x^2-12x$$ from here we get $$yz=18-6x$$ dividing by $2$: $$\frac{yz}{2}=9-3x$$