Perimeter: Right-angled Triangle

For any triangle with sides $a$, $b$, and $c$, the perimeter is simply the sum of all three sides:

For a right-angled triangle with perpendicular legs $a$ and $b$, we can use the Pythagorean theorem ($a^2 + b^2 = c^2$) to find the hypotenuse $c = \sqrt{a^2 + b^2}$, and then calculate the perimeter.

Variables:
• $P$ = Perimeter
• $a$ = first perpendicular leg
• $b$ = second perpendicular leg
• $c$ = hypotenuse

Derivation:
1. The perimeter of any triangle is the sum of its three sides: $P = a + b + c$.
2. For a right-angled triangle, if the hypotenuse $c$ is unknown, calculate it using the Pythagorean theorem: $c = \sqrt{a^2 + b^2}$.
3. Substitute $c$ back to find the perimeter.