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, is the triangle. Area of the triangle is

Second piece, is the circle. Area of the circle is

Therefore, total area can be expressed as .

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 , , and . Area of the triangle can be expressed as

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!