Substitute the known lengths of a right triangle's hypotenuse and one of its shorter sides into the Pythagorean formula. For example, if a triangle's hypotenuse is 5 inches and one of its sides is 3 inches, substitute 5 for "c" and 3 for "a" in the formula. This results in 3^2 + b^2 = 5^2.
Calculate a^2 and c^2 in the equation. For example, 3^2 equals 9 and 5^2 equals 25. This leaves 9 + b^2 = 25.
Subtract the number on the left side of the equation from both sides of the equation. For example, subtract 9 from both sides of the equation. This results in 9 + b^2 - 9 = 25 - 9, which leaves b^2 = 16.
Calculate the square root of both sides of the equation to solve for b. The square root of b^2 is b and the square root of 16 is 4, which leaves b = 4. Therefore, the length of b is 4 inches.
Add all three sides of the triangle to determine its perimeter. The sum of 3, 4 and 5 equals a perimeter of 12 inches.