The perimeter of a triangle with vertices (0, 4); (0, 0) and (3, 0) is:

To find the perimeter of a triangle with given vertices, we first need to find the length of each side using the distance formula, which is √[(x₂ - x₁)² + (y₂ - y₁)²].

The vertices of the triangle are (0, 4), (0, 0), and (3, 0).

Let's find the length of each side:

1. Side 1 (between (0, 4) and (0, 0)): Length = √[(0 - 0)² + (4 - 0)²] = √[0 + 16] = √16 = 4 units

2. Side 2 (between (0, 0) and (3, 0)): Length = √[(3 - 0)² + (0 - 0)²] = √[9 + 0] = √9 = 3 units

3. Side 3 (between (3, 0) and (0, 4)): Length = √[(3 - 0)² + (0 - 4)²] = √[9 + 16] = √25 = 5 units

Now, add up the lengths of the sides to find the perimeter:

Perimeter = Side 1 + Side 2 + Side 3 = 4 units + 3 units + 5 units = 12 units

So, the perimeter of the triangle is 12 units.