The area of a right triangle is 240 `cm^(2)` and one of its legs is 16 cm long . Find the length of the other leg .

Answer

To find the length of the other leg of the right triangle, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Area Formula**: The area \( A \) of a right triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
In this case, the legs of the triangle can be considered as the base and height.

2. **Identify Given Values**: From the problem, we know:
- Area \( A = 240 \, \text{cm}^2 \)
- One leg (base) \( = 16 \, \text{cm} \)
- Let the other leg (height) be \( x \, \text{cm} \).

3. **Set Up the Equation**: Substitute the known values into the area formula:
\[ 240 = \frac{1}{2} \times 16 \times x \]

4. **Simplify the Equation**: Multiply both sides by 2 to eliminate the fraction:
\[ 480 = 16 \times x \]

5. **Solve for \( x \)**: Divide both sides by 16 to find the length of the other leg:
\[ x = \frac{480}{16} \]

6. **Calculate the Value**: Perform the division:
\[ x = 30 \, \text{cm} \]

### Final Answer:
The length of the other leg is \( 30 \, \text{cm} \).

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