It seems you've uploaded an image containing a geometry problem, specifically involving a triangle with line segments and proportionality. I'll analyze the text and equations in the image to provide a solution.

Step-by-step interpretation and solution:

1. Geometry and Setup:

   • The triangle $\triangle ABC$ is provided with point $P$ dividing one of the sides.
   • Segment $AP$, $BP$, and $CP$ are involved.
   • The goal is to calculate the length of $CP$ using the given proportions and geometric relationships.

2. Proportionality:

   • From the image, it appears that the relationship $\frac{AP}{1.5} = \frac{CP}{3}$ is used.
   • This equation helps establish proportionality between the line segments.

3. Solving for $CP$:

   • Using the proportion: $\frac{AP}{1.5} = \frac{CP}{3}$
   • Cross multiply: $3 \cdot AP = 1.5 \cdot CP$
   • Rearrange: $CP = \frac{3 \cdot AP}{1.5}$
   • Simplify: $CP = 2 \cdot AP$

4. Given Value of $AP$:

   • From the diagram, $AP = 1.5$.
   • Substitute $AP$: $CP = 2 \cdot 1.5 = 3$

Final Answer:

The length of $CP$ is 3 units.

Would you like further details or explanations about any specific part of the problem?

5 Related Questions:

1. How can we use similar triangles to solve such proportionality problems?
2. What is the importance of cross-multiplication in solving proportions?
3. Could there be other methods to find $CP$ in this scenario?
4. How would the result change if $AP$ were a different length?
5. How can geometric theorems like Menelaus' theorem apply here?

Tip:

Always check for proportionality relationships in triangles and segments when dealing with geometric problems; they often simplify calculations significantly.