The height of a parallelogram is three-eighths of its base. If the area of the parallelogram is `96cm^(2)` , find its height and base .

Answer

To solve the problem, we need to find the height and base of a parallelogram given that the height is three-eighths of its base and the area is 96 cm².

### Step-by-Step Solution:

1. **Define Variables**:
Let the base of the parallelogram be \( b \) cm. According to the problem, the height \( h \) is given as:
\[ h = \frac{3}{8}b \]

2. **Area of the Parallelogram**:
The area \( A \) of a parallelogram is calculated using the formula:
\[ A = \text{base} \times \text{height} \]
Substituting the values we have:
\[ 96 = b \times h \]
Now, substituting \( h \) from the first step:
\[ 96 = b \times \left(\frac{3}{8}b\right) \]

3. **Simplify the Equation**:
This simplifies to:
\[ 96 = \frac{3}{8}b^2 \]
To eliminate the fraction, multiply both sides by 8:
\[ 768 = 3b^2 \]

4. **Solve for \( b^2 \)**:
Now, divide both sides by 3:
\[ b^2 = \frac{768}{3} = 256 \]

5. **Find \( b \)**:
Taking the square root of both sides gives:
\[ b = \sqrt{256} = 16 \text{ cm} \]

6. **Find \( h \)**:
Now, substitute \( b \) back into the equation for height:
\[ h = \frac{3}{8} \times 16 = 6 \text{ cm} \]

### Final Answer:
- Base \( b = 16 \) cm
- Height \( h = 6 \) cm