I have a test tomorrow and I'd really appreciate it if someone could check whether my work (just the relevant equation will do) is correct as I do not have an answer key.

1) A piece of wire 100cm long is cut into two pieces. One piece is bent to form a circle and the other piece is bent to form an equilateral triangle. How should the wire be cut so that the total enclosed area is a maximum/minimum.

First piece, $\displaystyle x$ is the triangle. Area of the triangle is $\displaystyle \displaystyle A(x)=(\frac{1}{2})(\frac{\sqrt{3}x}{6})(\frac{x}{3 })$

Second piece, $\displaystyle 100-x$ is the circle. Area of the circle is $\displaystyle \displaystyle A(x)=\frac{x^2-200x+10000}{4\pi}$

Therefore, total area can be expressed as $\displaystyle \displaystyle A(x)=\frac{\sqrt{3}}{36}x^2 + \frac{x^2-200x+10000}{4\pi}$.

Does that seem correct?

Another question that I'd appreciate checking is: An isosceles triangle has a perimeter of 48 cm, find the maximum area.

Sides of the triangle are $\displaystyle x$, $\displaystyle x$, and $\displaystyle y$. Area of the triangle can be expressed as $\displaystyle \displaystyle A(x)=(\frac{1}{2})(48-2x)(\sqrt{48x+576})$

If anyone can confirm whether any (don't have to do both of them if you can't) of the equations are correct, I'd greatly appreciate it!