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.

$\blacksquare$


Sources

  • 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 4$: Geometric Formulas: Rectangle of Length $b$ and Width $a$: $4.2$
  • 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 7$: Geometric Formulas: Rectangle of Length $b$ and Width $a$: $7.2.$
  • 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): perimeter
  • 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): perimeter
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