Let `DeltaABC~ DeltaDEF` and their areas be respectively 64 `cm^(2) ` and `121 cm^(2)` . If EF = 15.4 cm find BC .

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the relationship between the areas of similar triangles.
Since triangles ABC and DEF are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides.

### Step 2: Write down the areas of the triangles.
- Area of triangle ABC = 64 cm²
- Area of triangle DEF = 121 cm²

### Step 3: Set up the ratio of the areas.
Using the property of similar triangles:
\[ \frac{\text{Area of } \Delta ABC}{\text{Area of } \Delta DEF} = \left( \frac{BC}{EF} \right)^2 \]
Substituting the known values:
\[ \frac{64}{121} = \left( \frac{BC}{15.4} \right)^2 \]

### Step 4: Take the square root of both sides.
Taking the square root gives us:
\[ \sqrt{\frac{64}{121}} = \frac{BC}{15.4} \]
This simplifies to:
\[ \frac{8}{11} = \frac{BC}{15.4} \]

### Step 5: Cross-multiply to solve for BC.
Cross-multiplying gives:
\[ BC = 15.4 \times \frac{8}{11} \]

### Step 6: Calculate the value of BC.
Now we calculate:
\[ BC = 15.4 \times \frac{8}{11} = 15.4 \times 0.7272 \approx 11.2 \text{ cm} \]

### Final Answer:
Thus, the length of side BC is approximately **11.2 cm**.

---