Perimeter of Rectangle/Proof 1

Proof

 * PerimeterOfRectangle.png

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.