Perimeter of Triangle

Theorem

Let $ABC$ be a triangle.

Then the perimeter $P$ of $ABC$ is given by:

$P = a + b + c$

where $a, b, c$ are the lengths of the sides of $ABC$.


Proof

The perimeter of a plane geometric figure is defined as the total length of the boundary.

By definition, the boundary of a triangle comprises the three sides of that triangle.

Hence the result.

$\blacksquare$


Sources

  • 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 4$: Geometric Formulas: Triangle of Altitude $h$ and Base $b$: $4.6$
  • 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 7$: Geometric Formulas: Triangle of Altitude $h$ and Base $b$: $7.6.$
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