Corresponding sides of two similar triangle are in the ratio of 2:3 . If the are of the smaller triangle is 48 `cm^(2)` find the area of the larger triangle .

Answer

To find the area of the larger triangle given that the corresponding sides of two similar triangles are in the ratio of 2:3 and the area of the smaller triangle is 48 cm², we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio of Sides**: The ratio of the corresponding sides of the two triangles is given as 2:3. This means that if we denote the sides of the smaller triangle as 2x, the sides of the larger triangle will be 3x.

2. **Use the Area Ratio Formula**: The areas of similar triangles are proportional to the square of the ratio of their corresponding sides. Therefore, if the ratio of the sides is \( \frac{2}{3} \), the ratio of the areas will be:
\[ \left(\frac{2}{3}\right)^2 = \frac{4}{9} \]

3. **Set Up the Equation**: Let the area of the larger triangle be \( A \). According to the area ratio, we can set up the equation:
\[ \frac{\text{Area of smaller triangle}}{\text{Area of larger triangle}} = \frac{4}{9} \]
Substituting the area of the smaller triangle (48 cm²):
\[ \frac{48}{A} = \frac{4}{9} \]

4. **Cross-Multiply to Solve for A**: Cross-multiplying gives:
\[ 4A = 48 \times 9 \]

5. **Calculate the Right Side**: Now calculate \( 48 \times 9 \):
\[ 48 \times 9 = 432 \]
So, we have:
\[ 4A = 432 \]

6. **Divide by 4**: To find \( A \), divide both sides by 4:
\[ A = \frac{432}{4} = 108 \]

7. **Conclusion**: The area of the larger triangle is \( 108 \, \text{cm}^2 \).

### Final Answer:
The area of the larger triangle is **108 cm²**.