Let $x$ represent the length of the base of the isosceles triangle, and each of the two legs is $x - 3$ cm.

Since the perimeter of a triangle is the sum of all its sides, we can set up the equation as follows:

$x + 2(x - 3) = 48$

Expanding and simplifying:

$x + 2x - 6 = 48$

$3x - 6 = 48$

Adding 6 to both sides:

$3x = 54$

Dividing by 3:

$x = 18$

So, the length of the base of the isosceles triangle is 18 cm.

Would you like more details on the solution, or do you have any questions?

Here are five related questions:

1. What would be the length of each leg in this triangle?
2. How would the base length change if the perimeter were increased?
3. Can you determine the area of this triangle if the height were given?
4. How would you approach this problem if the perimeter were unknown?
5. How does this problem change if each leg is longer than the base?

Tip: In problems involving relationships between sides, use variables to express all unknowns in terms of a single variable for efficient solving.