How to Find the Perimeter of a Triangle?

When only two sides of a right triangle are known: use the Pythagorean theorem, a² + b² = c², to find the missing side first, then add all three:

1. Identify the two known sides (the legs, or a leg and the hypotenuse).
2. Solve for the missing side: if the hypotenuse is unknown, c = √(a² + b²); if a leg is unknown, a = √(c² − b²).
3. Add all three sides to get the perimeter.

Example: a right triangle with legs 3 and 4. The hypotenuse is √(3² + 4²) = √25 = 5. Perimeter = 3 + 4 + 5 = 12.

When the triangle is plotted on a coordinate plane (given three points, not side lengths): find each side's length using the distance formula,

distance = √[(x₂ − x₁)² + (y₂ − y₁)²]

applied to each pair of vertices, then add the three distances together.

Example: for vertices A(0,0), B(4,0), and C(0,3): side AB = 4, side AC = 3, and side BC = √[(4−0)² + (0−3)²] = √25 = 5. Perimeter = 4 + 3 + 5 = 12.

A note on units: the perimeter is always expressed in the same linear unit as the sides (cm, inches, etc.), unlike area, which is squared.

The closest sibling pages are What Are Complementary Angles? and What Are Supplementary Angles?.

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