The perimeter of two similar triangles are 24 cm and 1 cm respectively. If one side of the first triangle is 10 cm, then the corresponding side of the second triangle is

Options

A. 9 cm
B. 20/3 cm
C. 16/3 cm
D. 5 cm

Answer

To solve the problem of finding the corresponding side of the second triangle, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- 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

2. **Set up the ratio of the perimeters**:
Since the triangles are similar, the ratio of their corresponding sides is equal to the ratio of their perimeters. This can be expressed as:
\[ \frac{P1}{P2} = \frac{S1}{S2} \]

3. **Substitute the known values into the ratio**:
\[ \frac{24}{16} = \frac{10}{S2} \]

4. **Cross-multiply to solve for S2**:
\[ 24 \cdot S2 = 10 \cdot 16 \]

5. **Calculate the right side**:
\[ 10 \cdot 16 = 160 \]
So, we have:
\[ 24 \cdot S2 = 160 \]

6. **Divide both sides by 24 to isolate S2**:
\[ S2 = \frac{160}{24} \]

7. **Simplify the fraction**:
- Divide both the numerator and the denominator by 8:
\[ S2 = \frac{20}{3} \]

8. **Final answer**:
The corresponding side of the second triangle is:
\[ S2 = \frac{20}{3} \text{ cm} \]