Question
Show that among all rectangles with an 8-m perimeter possible, the one with the largest area is a square.
Draw a diagram of the problem. Draw a rectangle with sides $\displaystyle x$ and $\displaystyle y$. The perimeter will always be $\displaystyle 2y+2x=8$. The area is $\displaystyle A=xy$. Can you see what you need to do now?
That's the best approach to solving optimization problems. Draw a diagram.
If you are still lost on how to solve it, I'll help you. But see if you can proceed from here.