**Given information:**
- Perimeter of the right angle triangle = 30 cm
- Area of the right angle triangle = 30 cm²

**Let's assume the sides of the right angle triangle:**
- Base = x cm
- Height = y cm
- Hypotenuse = z cm

**Using the Pythagorean theorem:**
In a right angle triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse.
So, we have the equation: x² + y² = z²

**Calculating the perimeter:**
Perimeter = x + y + z = 30 cm

**Calculating the area:**
Area = (1/2) * x * y = 30 cm²

**Solving the equations:**

1. From the perimeter equation, we can express z in terms of x and y:
z = 30 - x - y

2. Substituting the value of z in the Pythagorean theorem equation:
x² + y² = (30 - x - y)²

3. Simplifying the equation:
x² + y² = 900 - 60x - 60y + x² + 2xy + y²

4. Canceling out common terms:
2x² + 2y² - 2xy - 60x - 60y + 900 = 0

5. Dividing the equation by 2:
x² + y² - xy - 30x - 30y + 450 = 0

6. Rearranging the equation:
x² + y² - xy - 30x - 30y + 450 = 0

**Using the quadratic formula:**
This equation is in the form ax² + bx + c = 0, where a = 1, b = -30, and c = 450.

1. Calculating the discriminant:
Discriminant (D) = b² - 4ac = (-30)² - 4(1)(450) = 900 - 1800 = -900

2. Since the discriminant is negative, the equation has no real solutions. Therefore, there are no valid values for x and y that satisfy the given conditions.

Hence, it is not possible to find the sides of a right angle triangle with a perimeter of 30 cm and an area of 30 cm².