let

a = 8 cm

b = 10 cm

where a and b are legs of the right triangle

c = the hypotenuse of the right triangle

following Pythagorean Theorem

c^2 = a^2 + b^2

c^2 = 8^2 + 10^2

c^2 = 164

c = 164^0.5

c = 12.81 cm approximately

the perimeter of the right triangle is P = a + b + c

P = 8 + 10 + 12.81

P = 30.81 cm

the perimeter of the right triangle is 30.81 cm.