Problem Analysis:
Let the sides of the right angled triangle be a, b and c, where c is the hypotenuse. The area of the triangle is given by 1/2 * a * b, and the perimeter is given by a + b + c. We are given that the ratio of the area to perimeter is 3:2. Therefore, we have the equation:

(1/2 * a * b) / (a + b + c) = 3/2

Simplifying this equation, we get:

ab = 3(a + b + c)

We need to find the smallest integral values of a, b and c that satisfy this equation.

Solution:

Step 1: Start by assuming a value for a. Let's assume a = 1.

Step 2: Substitute the value of a into the equation ab = 3(a + b + c).

1b = 3(1 + b + c)

Simplifying, we get:

b = 3 + 3b + 3c

2b = 3 + 3c

Step 3: Rearrange the equation to isolate b.

2b - 3b = 3c - 3

-b = 3c - 3

Step 4: Divide both sides by -1 to make b positive.

b = 3 - 3c

Step 5: Substitute the value of b into the equation ab = 3(a + b + c).

1(3 - 3c) = 3(1 + (3 - 3c) + c)

Simplifying, we get:

3 - 3c = 3(4 - 2c)

3 - 3c = 12 - 6c

Step 6: Rearrange the equation to isolate c.

3c - 6c = 12 - 3

-3c = 9

c = -3/3

Since the sides of the triangle must be positive integers, the value of c is not valid.

Step 7: Try a different value for a. Let's assume a = 2.

Step 8: Repeat steps 2-6 using the new value of a.

2b = 3 + 3c

b = (3 + 3c) / 2

2(3 + 3c) = 3(2 + (3 + 3c) + c)

6 + 6c = 3(5 + 4c)

6 + 6c = 15 + 12c

6c - 12c = 15 - 6

-6c = 9

c = -9/6

Again, the value of c is not valid.

Step 9: Repeat steps 7-8 with different values of a until a valid integral solution is found.

Step 10: The smallest valid integral solution is a = 3, b = 4, c = 5.

Step 11: Calculate the perimeter of the triangle.

Perimeter = a + b + c = 3 + 4 + 5