Explanation

 Let’s find the lengths of all three sides using the distance formula:

A(0,4), B(0,0), C(3,0)

AB = √[(0−0)² + (4−0)²] = √[16] = 4

BC = √[(3−0)² + (0−0)²] = √[9] = 3

CA = √[(3−0)² + (0−4)²] = √[9 + 16] = √25 = 5

Perimeter = AB + BC + CA = 4 + 3 + 5 = 12