# Perimeter of Rectangle

## Theorem

Let $ABCD$ be a rectangle whose side lengths are $a$ and $b$.

The perimeter of $ABCD$ is $2 a + 2 b$.

## Proof 1

From Rectangle is Parallelogram, $ABCD$ is a parallelogram.

By Opposite Sides and Angles of Parallelogram are Equal it follows that:

$AB = CD$
$BC = AD$

The perimeter of $ABCD$ is $AB + BC + CD + AD$.

But $AB = CD = a$ and $BC = AD = b$.

Hence the result.

$\blacksquare$

## Proof 2

From Rectangle is Parallelogram, $ABCD$ is a parallelogram.

The result then follows from a direct application of Perimeter of Parallelogram.

$\blacksquare$