1. The problem statement, all variables and given/known data A piece of wire, 100 cm long, needs to be bent to form a rectangle. Determine the dimensions of a rectangle with the maximum area. 2. Relevant equations P = 2(l+w) A = lw 3. The attempt at a solution This is what I don't understand, the solutions that I saw from looking around is: l = x w = (100 -2x) / 2 I don't understand why is width portrayed as shown above, and why the length is also potrayed as above, the solution goes onto: A = (x)(100 - 2x / 2) A = (x)(50 = x) A = 50x - x^2 A prime = 50 - x^2 Insert 0 for A prime 0 = 50 - x^2 x=25 With therefore means the length and width are 25cm. I understand the algebra, I do not understand how to get the length and width equation, wondering if someone could explain it to me.