Confusing Area Optimization problem

[jackz2003]

Attached is the problem. I can get the sketch down, but am confused as to how to translate it to a function/graph. We have not been taught related rates or area/volume optimization yet, so I am not sure what to do here.

 

[yoscar04]

Hi. What is the area of a rectangle? It is given to you that x is the length. Lets call the height h. Try to connect the perimeter of the rectangle that is 100 meter with x and h and find an expression for h(x). Then find the area A(x). Make a graph and you will get the answer of what you are looking for. If you get stuck we will help you, but show us what you can do by yourself.

 

[jackz2003]

Hi. What is the area of a rectangle? It is given to you that x is the length. Lets call the height h. Try to connect the perimeter of the rectangle that is 100 meter with x and h and find an expression for h(x). Then find the area A(x). Make a graph and you will get the answer of what you are looking for. If you get stuck we will help you, but show us what you can do by yourself.

I actually think I got it. A(x) should come out to x(50-x), or -x^2-50x. After that I can find the maximum optimized area and dimensions w/ the table function on my calculator.

 

[Steven G]

Good work! What dimension did you get for the rectangle? What happens if instead of the perimeter being 100 or 75 it was p. Can you figure out the dimensions?