If the base of a parallelogram is (x + 4), altitude to the base `(x-3)` and the area is `(x^(2)-4)` , then the actual area is equal to .

Options

A. 64 sq units
B. 48 sq units
C. 60 sq units
D. None of these

Answer

To find the actual area of the parallelogram given the base, altitude, and area expression, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Base \( b = x + 4 \)
- Altitude \( h = x - 3 \)
- Area \( A = x^2 - 4 \)

2. **Use the area formula for a parallelogram**:
The area of a parallelogram is given by the formula:
\[ A = \text{Base} \times \text{Height} \]
Therefore, we can write:
\[ x^2 - 4 = (x + 4)(x - 3) \]

3. **Expand the right side**:
Now, we will expand the right side:
\[ (x + 4)(x - 3) = x^2 - 3x + 4x - 12 = x^2 + x - 12 \]

4. **Set up the equation**:
Now we can set the two expressions for area equal to each other:
\[ x^2 - 4 = x^2 + x - 12 \]

5. **Simplify the equation**:
Subtract \( x^2 \) from both sides:
\[ -4 = x - 12 \]

6. **Solve for \( x \)**:
Add 12 to both sides:
\[ 12 - 4 = x \]
\[ x = 8 \]

7. **Calculate the actual area**:
Now substitute \( x = 8 \) back into the area formula:
\[ A = x^2 - 4 = 8^2 - 4 = 64 - 4 = 60 \]

8. **Final answer**:
Therefore, the actual area of the parallelogram is:
\[ \text{Area} = 60 \text{ square units} \]