The perimeters of two similar triangles are 25 cm and 15 cm respectively. If one side of the first triangle is 9 cm, then the corresponding side of second triangle is .........

Answer

To find the corresponding side of the second triangle, we can use the property of similar triangles, which states that the ratio of the perimeters of two similar triangles is equal to the ratio of their corresponding sides.

### Step-by-Step Solution:

1. **Identify the given values:**
- Perimeter of the first triangle (P1) = 25 cm
- Perimeter of the second triangle (P2) = 15 cm
- One side of the first triangle (S1) = 9 cm
- Let the corresponding side of the second triangle be S2.

2. **Set up the ratio of the perimeters:**
\[ \frac{P1}{P2} = \frac{S1}{S2} \]
Substituting the known values:
\[ \frac{25}{15} = \frac{9}{S2} \]

3. **Cross-multiply to solve for S2:**
\[ 25 \cdot S2 = 15 \cdot 9 \]

4. **Calculate the right side:**
\[ 15 \cdot 9 = 135 \]
So we have:
\[ 25 \cdot S2 = 135 \]

5. **Divide both sides by 25 to isolate S2:**
\[ S2 = \frac{135}{25} \]

6. **Simplify the fraction:**
\[ S2 = 5.4 \text{ cm} \]

### Final Answer:
The corresponding side of the second triangle is **5.4 cm**.