# The length of a rectangle is three times its width. If the perimeter is at most 112 centimeters, what is the greatest possible value for the width?

Nov 24, 2016

The greatest possible value for the width is 14 centimeters.

#### Explanation:

The perimeter of a rectangle is $p = 2 l + 2 w$ where $p$ is the perimeter, $l$ is the length and $w$ is the width.

We are given the length is three times the width or $l = 3 w$.

So we can substitute $3 w$ for $l$ in the formula for the perimeter of a rectangle to get:

$p = 2 \left(3 w\right) + 2 w$

$p = 6 w + 2 w$

$p = 8 w$

The problem also states the perimeter is at most 112 centimeters. At most means the perimeter is less than or equal to 112 centimeters. Knowing this inequality and know the perimeter can be expresses as $8 w$ we can write and solve for $w$:

$8 w \le 112$ centimeters

$\frac{8 w}{8} \le \frac{112}{8}$ centimeters

$w \le 14$ centimeters