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To solve this problem, let's define the variables and equations based on the given information:

1. Segment \( AD = 20 \, m \).
2. Segment \( BC = 5 \, m \).
3. Relation between segments: \(\frac{AB}{CD} = \frac{2}{3}\).

Let \( AB = x \) and \( CD = 20 - x - 5 = 15 - x \) because the total length of \( AD \) is 20 meters.

### Step-by-Step Solution

Given the ratio:

\[
\frac{AB}{CD} = \frac{2}{3}
\]

Substituting the values:

\[
\frac{x}{15 - x} = \frac{2}{3}
\]

Cross-multiply to solve for \( x \):

\[
3x = 2(15 - x)
\]

Simplify:

\[
3x = 30 - 2x
\]

Combine like terms:

\[
3x + 2x = 30
\]

\[
5x = 30
\]

\[
x = 6
\]

So, the value of \( x \) is \( 6 \, m \).

### Answer

The correct answer is:

- \( x = 6 \, m \).

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

### Related Questions

1. How would the problem change if the ratio of \( AB \) to \( CD \) was \(\frac{3}{2}\)?
2. What if the length of \( BC \) was 10 m? How would this affect the value of \( x \)?
3. How can you check if your solution is correct using substitution?
4. What if the total length of \( AD \) was unknown? How would you approach the problem?
5. How would you solve this problem if the relationship between segments was given in decimals?

**Tip**: Always double-check your setup of equations when dealing with ratios and segment lengths.

Determinar el valor de 'x', sabiendo que la longitud del segmento AD es 20 m y la del segmento BC es 5 m. Además, considerar que la relación entre los segmentos AB y CD es 2/3.

Solve the problem where the value of 'x' must be determined given that the length of segment AD is 20 meters, BC is 5 meters, and the ratio AB to CD is 2/3. Learn the step-by-step process of solving this algebraic and geometric problem, suitable for Grades 8-10.

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