Similar Triangles Analysis: Finding Similarity Ratio Among Three Given Triangles

To solve the problem, we proceed with the following steps:

• Identify the given side lengths for each triangle.
• Compare the side ratios of each triangle pair to check for similarity.
• Verify the side ratios to affirm the similarity ratio.
• Select the correct multiple-choice answer based on the analysis.

Given side lengths:
Triangle C: $6$, $3$, $3$ (perpendicular and base, as seen in figure).
Triangle B: $4.5$, $3$, $2$ (perpendicular and base, as seen in figure).
Triangle A: $6$, $4$, $3.5$ (perpendicular and base, as seen in figure).

Calculating the ratios:

• For triangles C and B:
  $\frac{6}{4.5} = \frac{3}{2}$ which simplifies to $\frac{3}{2} = 1.5$, indicating that triangles C and B are similar.
• Comparison for other pairs: Triangle A with Triangle B or C reveals no common proportionality.

Therefore, the only pair of similar triangles is C and B with a similarity ratio of $\frac{3}{2}$ or 1.5.

The correct choice is, therefore, C + B are similar with a ratio of 1.5.