The perimeters of two similar triangles are 30 and 20 cm respectively side of first triangle is 9 cm. Determine the corresponding side of the second triangle.

Options

A. 13.5 cm
B. 6 cm
C. 15 cm
D. 5 cm

Answer

To solve the problem, we need to use the property of similar triangles, which states that the ratios of the corresponding sides of similar triangles are equal to the ratios of their perimeters.

### Step-by-Step Solution:

1. **Identify the given values:**
- Perimeter of the first triangle (P1) = 30 cm
- Perimeter of the second triangle (P2) = 20 cm
- One side of the first triangle (S1) = 9 cm
- Corresponding side of the second triangle (S2) = ?

2. **Set up the ratio of the perimeters:**
Since the triangles are similar, we can write the ratio of their perimeters as:
\[ \frac{P1}{P2} = \frac{S1}{S2} \]
Substituting the known values:
\[ \frac{30}{20} = \frac{9}{S2} \]

3. **Simplify the ratio of the perimeters:**
The ratio \( \frac{30}{20} \) can be simplified:
\[ \frac{30}{20} = \frac{3}{2} \]
So, we have:
\[ \frac{3}{2} = \frac{9}{S2} \]

4. **Cross-multiply to solve for S2:**
Cross-multiplying gives us:
\[ 3 \cdot S2 = 2 \cdot 9 \]
Simplifying the right side:
\[ 3 \cdot S2 = 18 \]

5. **Divide both sides by 3 to isolate S2:**
\[ S2 = \frac{18}{3} = 6 \text{ cm} \]

### Final Answer:
The corresponding side of the second triangle is **6 cm**.