Geometry

Question Analysis  

This question involves the Perimeters of Similar Shapes, focusing on applying the direct proportionality of perimeters in similar triangles to find an unknown perimeter.  

 

Key Concept Explanation:  

For similar triangles, the ratio of perimeters equals the ratio of their corresponding side lengths (scale factor). If the similarity ratio is  (larger:smaller), the perimeter ratio remains .  

 

Step-by-Step Solution:  

1. Let the perimeter of the smaller triangle be .  

2. Set up the proportion using the given ratio  (smaller:larger is , so larger:smaller is ):  

  

3. Cross-multiply to solve for :