The bases of the trapezoid are 2: 3 and the middle line is 20. Find the smaller base.

1. Let’s denote one part by x.

2. Define the smaller base of the trapezoid:

2 * x = 2x.

3. Recognize the larger base of the trapezoid:

3 * x = 3x.

4. Let’s compose and solve the equation:

(2x + 3x) / 2 = 20;

(5x) / 2 = 20;

5x = 20 * 2;

5x = 40;

x = 40: 5;

x = 8.

5. One part is equal to x = 8.

6. What is the smaller base of the trapezoid?

2 * x = 2 * 8 = 16.

Answer: the smaller base of the trapezoid is 16.