`DeltaABC ~ DeltaDEF`. Their areas are `64 cm^2 and 121cm^2`. If `EF = 12.1 cm`, then value of BC is :

Options

A. 8.8 cm
B. 12.1
C. 12.4 cm
D. None of these

Answer

To solve the problem, we will use the properties of similar triangles and the relationship between their areas and corresponding sides.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Area of triangle ABC = 64 cm²
- Area of triangle DEF = 121 cm²
- Length of side EF = 12.1 cm

2. **Use the Ratio of Areas:**
Since triangles ABC and DEF are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides. Therefore, we can write:
\[ \frac{\text{Area of } \Delta ABC}{\text{Area of } \Delta DEF} = \left(\frac{BC}{EF}\right)^2 \]

3. **Substituting the Areas:**
Substitute the given areas into the equation:
\[ \frac{64}{121} = \left(\frac{BC}{12.1}\right)^2 \]

4. **Taking the Square Root:**
Taking the square root of both sides gives:
\[ \frac{\sqrt{64}}{\sqrt{121}} = \frac{BC}{12.1} \]
Simplifying the square roots:
\[ \frac{8}{11} = \frac{BC}{12.1} \]

5. **Cross-Multiplying to Solve for BC:**
Now we cross-multiply to find BC:
\[ 8 \cdot 12.1 = 11 \cdot BC \]
\[ 96.8 = 11 \cdot BC \]

6. **Dividing to Isolate BC:**
Now, divide both sides by 11:
\[ BC = \frac{96.8}{11} \]
Calculating this gives:
\[ BC = 8.8 \text{ cm} \]

### Final Answer:
The length of side BC is **8.8 cm**.

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