In right △ABC , the right angle is at C, m∠A=30∘ , and AC=5√ 5 units.

What is the perimeter of △ABC ?

Using the 30-60-90 right triangle theorum,

the hypothenuse is 5 sqrt(5)

BC is the 5 sqrt(5) / 2

AC is then 5 sqrt(15) / 2

add them up and you get

15 sqrt(5) / 2 + 5 sqrt(15) / 2