In a parallelogram ABCD, AB = 12 cm and the altitude corresponding to AB is 8 cm. If AD= 10 cm, then the altitude corresponding to AD is equal to

Options

A. 8.5 cm
B. 9 cm
C. 9.6 cm
D. 10.8 cm

Answer

To find the altitude corresponding to side AD in parallelogram ABCD, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Length of side AB (base) = 12 cm
- Altitude corresponding to AB = 8 cm
- Length of side AD = 10 cm
- Altitude corresponding to AD = x (this is what we need to find)

2. **Calculate the area of the parallelogram using AB and its corresponding height**:
\[ \text{Area} = \text{Base} \times \text{Height} = AB \times \text{Altitude corresponding to AB} \]
\[ \text{Area} = 12 \, \text{cm} \times 8 \, \text{cm} = 96 \, \text{cm}^2 \]

3. **Set up the equation for the area using AD and its corresponding height**:
\[ \text{Area} = AD \times \text{Altitude corresponding to AD} \]
\[ \text{Area} = 10 \, \text{cm} \times x \]

4. **Equate the two expressions for the area**:
\[ 10 \, \text{cm} \times x = 96 \, \text{cm}^2 \]

5. **Solve for x**:
\[ x = \frac{96 \, \text{cm}^2}{10 \, \text{cm}} = 9.6 \, \text{cm} \]

6. **Conclusion**:
The altitude corresponding to side AD is 9.6 cm.

### Final Answer:
The altitude corresponding to AD is **9.6 cm**.

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