The in-radius of a triangle is 6 cm, and the sum of the lengths of its side is 50 cm. The area of the triangle (in square cm.) is

Options

A. 150
B. 50
C. 300
D. 56

Answer

To find the area of the triangle using the given in-radius and the sum of the lengths of its sides, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- In-radius (r) = 6 cm
- Sum of the lengths of the sides (a + b + c) = 50 cm

2. **Use the formula for the area of a triangle:**
The area (A) of a triangle can be calculated using the formula:
\[ A = r \times \frac{(a + b + c)}{2} \]
where \( r \) is the in-radius and \( (a + b + c) \) is the sum of the lengths of the sides.

3. **Substitute the known values into the formula:**
- Substitute \( r = 6 \) cm and \( a + b + c = 50 \) cm into the formula:
\[ A = 6 \times \frac{50}{2} \]

4. **Calculate the sum of the sides divided by 2:**
- Calculate \( \frac{50}{2} = 25 \).

5. **Multiply the in-radius by the result:**
- Now, calculate the area:
\[ A = 6 \times 25 = 150 \text{ square cm} \]

### Final Answer:
The area of the triangle is **150 square cm**.

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