The base of the trapezoid is 2: 3 and the middle line is 25. Find the smaller base.

1. Let’s denote one part by x.

2. Determine the length of the smaller base of the trapezoid:

2 * x = 2x.

3. Find out the length of the larger base of the trapezoid:

3 * x = 3x.

4. Since the middle line of the trapezoid is 25, compose and solve the equation:

(2x + 3x) / 2 = 25;

5x = 25 * 2;

5x = 50;

x = 50: 5;

x = 10.

5. One part is equal to x = 10.

6. What is the length of the smaller base of the trapezoid?

2 * 10 = 20.

Answer: The length of the smaller base of the trapezoid is 20.