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?

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Answer 1 · 2016-11-11T13:30:29

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

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:

$p = 2*l + 2*w$ 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:

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

Simplifying this equation gives:

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

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

$p = 12x - 9$