**Given Information**
- Altitude of the triangle = 7 cm less than the base.
- Hypotenuse of the triangle = 13 cm.

To find the other two sides of the triangle, we need to determine the lengths of the base and the altitude.

**Understanding the Problem**
We are given a right triangle, where the altitude is less than the base by 7 cm. The hypotenuse of the triangle is also given. We need to find the lengths of the base and the altitude.

**Solution**
Let's assume the base of the triangle as 'b' cm.
According to the given information, the altitude of the triangle is 7 cm less than the base. Therefore, the altitude can be represented as (b - 7) cm.

**Applying Pythagoras Theorem**
In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Using this theorem, we can write the equation as follows:
(b^2) + ((b - 7)^2) = (13^2)

**Solving the Equation**
Expanding the equation and simplifying, we get:
b^2 + (b^2 - 14b + 49) = 169

Combining like terms, we have:
2b^2 - 14b + 49 - 169 = 0

Simplifying further, we get the quadratic equation:
2b^2 - 14b - 120 = 0

Factoring the quadratic equation, we have:
2(b^2 - 7b - 60) = 0

(b - 12)(2b + 5) = 0

Hence, we have two possible solutions for 'b':
- b - 12 = 0, which gives b = 12 cm
- 2b + 5 = 0, which gives b = -2.5 cm (not a valid solution)

Therefore, the base of the triangle is 12 cm.

**Finding the Altitude**
We know that the altitude is 7 cm less than the base.
So, the altitude can be calculated as follows:
Altitude = base - 7 = 12 - 7 = 5 cm

**Final Answer**
The base of the triangle is 12 cm and the altitude is 5 cm.