Perimeter of Rectangle/Proof 1
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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.
$\blacksquare$