# The width of a rectangular garage is 8 feet less than the length. How do you express the perimeter of the garage as a function of the length?

Feb 26, 2017

$P = 4 \left(l - 4\right)$

#### Explanation:

We can call the length of the garage $l$.

Therefore the width, or we can call it $w$, of the garage is $l - 8$ or $w = l - 8$

The formula for the perimeter of a rectangle is:

$P = 2 \left(w + l\right)$

We can substitute $l - 8$ for $w$ giving:

$P = 2 \left(l - 8 + l\right) \to$

$P = 2 \left(l + l - 8\right) \to$

$P = 2 \left(2 l - 8\right) \to$

$P = 2 \left(2 \left(l - 4\right)\right) \to$

$P = 4 \left(l - 4\right)$