Right Triangle Perimeter

Part of the Triangles section of Coddy's Geometry journey. Lesson 65 of 71.

The perimeter of a triangle is the sum of its three sides. When you know only the two legs of a right triangle, first find the hypotenuse with the Pythagorean theorem. Take legs 6 and 8:

$A right triangle with legs 8 and 6 and hypotenuse c$

Legs 6 and 8: the third side comes from the theorem

P = 6 + 8 + √(6^2 + 8^2)

P = 6 + 8 + √(100)

P = 6 + 8 + 10 = 24

The hypotenuse is 10, and the three sides add to 24.

You can write the whole calculation in one line, with the root for the hypotenuse inside the sum. Sometimes the root is not a whole number. Then the perimeter keeps the root. Legs 1 and 2 give P = 3 + √(5). The perimeter 3 + √(5) is exact, and it cannot be simplified further.