Answer:
The maximum possible area of the triangle is 36 units²
Step-by-step explanation:
Let
x, y the legs of the right triangle
Applying the Pythagoras Theorem
[tex]12^{2}=x^{2}+y^{2}\\\\144=x^{2}+y^{2}[/tex]
[tex]y=\sqrt{144-x^{2}}[/tex] ----> equation A
The area of the right triangle is equal to
[tex]A=\frac{1}{2}xy[/tex] ----> equation B
substitute equation A in equation B
[tex]A=\frac{1}{2}x(\sqrt{144-x^{2}})[/tex]
Using a graphing tool
The vertex of the graph is a maximum
That means
The x-coordinate of the vertex is the value of x for the maximum possible area of the triangle
The y-coordinate of the vertex is the maximum possible area of the triangle
The vertex is the point (8.485,36)
see the attached figure
therefore
The maximum possible area of the triangle is 36 units²
