Maximum dimensions

Question

I just recieved an assignment to find the maximum area of a rectangle when there are 100 feet of fencing availabe. You plan on using your neighbors fence for one side. The equations for the area, length, and width of the rectangle are listed below:
Area=X(100-2X)
Length= 100-2X
Width=X
I am trying to obtain the largest rectangular area possible. I have already found out how to find the largest area possible, my trouble is in finding the dimensions. I should get a 25 by 50 rectangle and yet I just can't seen to figure out how to get those dimensions. The focus of the assignment is using ifs.
Heres my code for the maximum area:
public class Prog215c
public static void main (String [] args)
int x, area, maxAREA, length, width;
maxAREA=0;
for (x=1; x<=100; x++)
area= x * (100 - (2 * x));
if (area>maxAREA)
maxAREA=area;
System.out.println(maxAREA);
Would anyone mind pointing me in the right direction? I'm a complete beginner at java so I hope you don't mind what I know is probably a question with a very simple answer. Thanks for your help in advance. This is my first post too in these forums too ^^

Answer 1

Hi Firesword,
The problem is that by the time your loop finishes,
you don't really have an "x" with a sensible value you
can use.
Consider the following fragment
int resultArea = -1;
int resultWidth = -1;
for(int x =0; x <= 50; x++) {
    int area = x * (100 - (2 * x));
    if(area > resultArea) {
        resultArea = area;
        resultWidth = x;
}Now you can System.out.print resultWidth as well as resultArea.
(You can call it resultLength if you prefer, the question is
symmetrical wrt length and width).
Since you only have 100m of wire, I don't recommend letting
the width get bigger than 50m, or you'll run out wire!
Cheers,
Peter