Given information:
Perimeter = 120
Base = 20

Introduction:
To find the height of a triangle, we need to use the formula for the perimeter of a triangle and the relationship between the base and height of a triangle.

Formula:
The perimeter of a triangle is calculated by adding the lengths of all three sides. In this case, we are given the perimeter as 120, so we can write the equation as:
Perimeter = Side1 + Side2 + Side3

Step 1: Calculate the perimeter:
Since we know the base is 20, and the other two sides are unknown, let's assume the other two sides as Side1 and Side2. We can write the equation as:
120 = 20 + Side1 + Side2

Step 2: Find the remaining side length:
To find the remaining side length, we need to subtract the base length from the perimeter and divide the result by 2. This is because the remaining two sides of a triangle are equal in an isosceles triangle (which is the case here).
Remaining side length = (Perimeter - Base length) / 2
Remaining side length = (120 - 20) / 2
Remaining side length = 100 / 2
Remaining side length = 50

Step 3: Calculate the height:
The height of a triangle can be found using the formula:
Area = (Base * Height) / 2

Since we know the base is 20 and the area is equal to half the product of the base and height, we can write the equation as:
Area = (20 * Height) / 2

Step 4: Calculate the area:
We can calculate the area of a triangle using the formula:
Area = √(s * (s - Side1) * (s - Side2) * (s - Side3))

where s is the semi-perimeter calculated as:
s = (Side1 + Side2 + Side3) / 2

Substituting the values we have:
Area = √(s * (s - 20) * (s - 50) * (s - 50))

Step 5: Solve for the height:
Now we can solve the equation for height. Rearranging the equation, we have:
(20 * Height) / 2 = √(s * (s - 20) * (s - 50) * (s - 50))

Simplifying further:
Height = (2 * √(s * (s - 20) * (s - 50) * (s - 50))) / 20

Conclusion:
By solving the equation, we can find the height of the triangle.