The perimeter of two similar triangles are 24cm and 16cm, respectively. If one side of the first triangle is 10cm, then the corresponding side of the second triangle is

Answer

To solve the problem step by step, we will use the properties of similar triangles and the given information about their perimeters and one side of the first triangle.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Perimeter of the first triangle (P1) = 24 cm
- Perimeter of the second triangle (P2) = 16 cm
- One side of the first triangle (S1) = 10 cm
- Corresponding side of the second triangle (S2) = x (unknown)

2. **Write the Ratio of the Perimeters:**
Since the triangles are similar, the ratio of their perimeters is equal to the ratio of their corresponding sides.
\[ \frac{P1}{P2} = \frac{S1}{S2} \]
Substituting the known values:
\[ \frac{24}{16} = \frac{10}{x} \]

3. **Cross-Multiply to Solve for x:**
Cross-multiplying gives us:
\[ 24x = 16 \times 10 \]
Simplifying the right side:
\[ 24x = 160 \]

4. **Isolate x:**
Now, divide both sides by 24 to solve for x:
\[ x = \frac{160}{24} \]

5. **Simplify the Fraction:**
To simplify \( \frac{160}{24} \), we can divide both the numerator and the denominator by their greatest common divisor, which is 8:
\[ x = \frac{160 \div 8}{24 \div 8} = \frac{20}{3} \]

6. **Convert to Decimal (if needed):**
If we want to express \( \frac{20}{3} \) in decimal form:
\[ x \approx 6.67 \text{ cm} \]

### Final Answer:
The corresponding side of the second triangle is approximately \( 6.67 \) cm.

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