# The length of a rectangle is 4x+3 and the width is 2x-6, how do you write the expression for the perimeter of the rectangle?

Nov 11, 2016

$p = 2 \left(4 x + 3\right) + 2 \left(2 x - 6\right)$ or simplified $p = 12 x - 9$

#### Explanation:

By definition the perimeter of an object is the length of all its sides.

Also by definition, for a rectangle the 2 sides of the width are equal and the 2 sides of the length are equal.

Therefore the equation for the perimeter of a rectangle can be written as:

$p = 2 \cdot l + 2 \cdot w$ where $p$ is the perimeter, $l$ is the length and $w$ is the width.

Substituting what was given about the length and width gives the equation:

$p = 2 \left(4 x + 3\right) + 2 \left(2 x - 6\right)$

Simplifying this equation gives:

$p = 8 x + 3 + 4 x - 12$

$p = 8 x + 4 x + 3 - 12$

$p = 12 x - 9$