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## Homework Statement

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.

## Homework Equations

P = 2(l+w)

A = lw

## 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.