I recently took a maths test where one of the questions was just unsolvable for me. I'm going to try to make it as clear as possible, to not create confusion.
The question looks like this:
"A rectangle shape, which has one of it's sides replaced by a half circle (see picture above.) has a circumference of 100 meters.
What is the maximum possible area of this shape?"
The test was about quadratic equations, parabolas, and their graphs.
How would you solve this kind of question? I would really appreciate all help I could get!
Let the sidelength of the rectangle be $x$ respectively $y$, then the area is given by $$A=xy-\frac{\pi y^2}{8}$$ and the perimeter is given by $$p=2x+y+\frac{\pi y}{2}$$ Can you proceed now?