Function Problem: Area of Rectangle with 100ft Perimeter

[Arreat]

Homework Statement

Express the area of a rectangle with the perimeter of 100 feet as a function of the lengh L of one of its sides

Homework Equations

100=2w+2l

The Attempt at a Solution

As far as I can get is,

L = 50 -2w

Just writing the function is a problem, I assume it's something like but I'm not sure, sorry if I'm completely off it's been a long day.
A(W) = (50-2w)(w) = 50w - 2w^2
or
A = w(50-w)

 

[symbolipoint]

You successfully wrote the function for area (in two equivalent forms).

 

[Mentallic]

If $$100=2L+2W$$

then $$L=50-W$$ but $$L\neq 50-2W$$

Therefore your 2nd equation for the function is the correct one. $$A=-W^2+50W$$

But the question asked as a function of the length, not width. It will be similar though. Just make width the subject of the perimeter equation and substitute into the area formula.