###### Example3.1.12

Virginia is designing a rectangular garden. The garden's length must be $$4$$ meters less than three times the width, and its perimeter must be $$40$$ meters. Find the garden's length and width.

Reminder: A rectangle's perimeter formula is $$P=2(L+W)\text{,}$$ where $$P$$ stands for perimeter, $$L$$ stands for length and $$W$$ stands for width.

Assume the rectangle's width is $$W$$ meters. We can then represent the length as $$3W-4$$ meters since we are told that it is $$4$$ meters less than three times the width. It's given that the perimeter is $$40$$ meters. Substituting those values into the formula, we have:

\begin{align*} P\amp=2(L+W)\\ 40\amp=2(3W-4+W)\\ 40\amp=2(4W-4)\amp\text{Like terms were combined.} \end{align*}

The next step to solve this equation is to remove the parentheses by distribution.

To check this result, we'll want to replace $$6$$ in the equation $$40=2(4W-4)\text{:}$$
To determine the length, recall that this was represented by $$3W-4\text{,}$$ which is:
Thus the rectangle's width is $$6$$ meters and the length is $$14$$ meters.