Given information:
- Area of right angle triangle = 30 cm
- Length of hypotenuse = 13 cm

To find:
- Length of shorter leg

Explanation:
Let's assume the two legs of the right angle triangle are represented by 'a' and 'b', and the hypotenuse is represented by 'c'. According to the Pythagorean theorem, the relationship between the sides of a right angle triangle is given by the equation: a^2 + b^2 = c^2.

Step 1: Finding the longer leg
Since we know the area of the triangle, we can use the formula for the area of a right angle triangle, which is given by the equation: Area = (1/2) * base * height.

In a right angle triangle, the two legs act as base and height. Therefore, we can rewrite the equation as: Area = (1/2) * a * b.

Substituting the given area (30 cm) into the equation, we get: 30 = (1/2) * a * b.

Step 2: Finding the longer leg using the hypotenuse
We can use the relationship between the legs and the hypotenuse to find the longer leg. According to the Pythagorean theorem: a^2 + b^2 = c^2.

Substituting the given hypotenuse (13 cm) into the equation, we get: a^2 + b^2 = 13^2.

Step 3: Solving the equations simultaneously
We have two equations:
1) 30 = (1/2) * a * b
2) a^2 + b^2 = 13^2

We can solve these equations simultaneously to find the values of 'a' and 'b'.

Step 4: Finding the shorter leg
Once we have the values of 'a' and 'b', we can determine which one is the shorter leg. The shorter leg is the side opposite the smaller angle in a right angle triangle.

Conclusion:
By solving the equations simultaneously, we can find the values of 'a' and 'b', which represent the lengths of the two legs of the right angle triangle. The shorter leg can then be determined based on the values obtained.