If the perimeters of two similar triangles ABC and DEF are 50 cm and 70 cm respectively and one side of ∆ABC = 20 cm, then find the corresponding side of ∆DEF

Answer

To find the corresponding side of triangle DEF, we can use the property of similar triangles, which states that the ratios of the corresponding sides are equal to the ratios of their perimeters.

### Step-by-Step Solution:

1. **Identify the given information:**
- Perimeter of triangle ABC = 50 cm
- Perimeter of triangle DEF = 70 cm
- One side of triangle ABC (let's say AB) = 20 cm
- We need to find the corresponding side of triangle DEF (let's say DE).

2. **Set up the ratio of the perimeters:**
Since the triangles are similar, we can set up the following proportion:
\[ \frac{\text{Perimeter of } ABC}{\text{Perimeter of } DEF} = \frac{AB}{DE} \]
Substituting the known values:
\[ \frac{50}{70} = \frac{20}{DE} \]

3. **Cross-multiply to solve for DE:**
Cross-multiplying gives us:
\[ 50 \cdot DE = 70 \cdot 20 \]

4. **Calculate the right side:**
\[ 70 \cdot 20 = 1400 \]
So we have:
\[ 50 \cdot DE = 1400 \]

5. **Isolate DE:**
To find DE, divide both sides by 50:
\[ DE = \frac{1400}{50} \]

6. **Perform the division:**
\[ DE = 28 \text{ cm} \]

### Final Answer:
The corresponding side of triangle DEF (DE) is **28 cm**.