Perimeter of Rectangle/Proof 1

Theorem

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

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

Proof

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.

$\blacksquare$