Two sides of a parallelogram are 20 cm and 25 cm. If the altitude corresponding to the side of length 25 cm is 10 cm, then the altitude corresponding to the other pair of sides is

Options

A. 10.5 cm
B. 12 cm
C. 12.5 cm
D. 10 cm

Answer

To find the altitude corresponding to the side of length 20 cm in a parallelogram where the sides are 20 cm and 25 cm, and the altitude corresponding to the side of length 25 cm is 10 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Side 1 (Base 1) = 25 cm
- Altitude corresponding to Base 1 (Height 1) = 10 cm
- Side 2 (Base 2) = 20 cm
- Altitude corresponding to Base 2 (Height 2) = x (unknown)

2. **Calculate the Area of the Parallelogram**:
The area of a parallelogram can be calculated using the formula:
\[ \text{Area} = \text{Base} \times \text{Height} \]
For Base 1 (25 cm) and Height 1 (10 cm):
\[ \text{Area} = 25 \, \text{cm} \times 10 \, \text{cm} = 250 \, \text{cm}^2 \]

3. **Set Up the Equation for the Area Using Base 2**:
Now, we will express the area using Base 2 (20 cm) and the unknown Height 2 (x):
\[ \text{Area} = 20 \, \text{cm} \times x \]

4. **Equate the Two Area Expressions**:
Since both expressions represent the same area, we can set them equal to each other:
\[ 20 \, \text{cm} \times x = 250 \, \text{cm}^2 \]

5. **Solve for x**:
To find x, divide both sides by 20 cm:
\[ x = \frac{250 \, \text{cm}^2}{20 \, \text{cm}} = 12.5 \, \text{cm} \]

6. **Conclusion**:
The altitude corresponding to the side of length 20 cm is 12.5 cm.

### Final Answer:
The altitude corresponding to the side of length 20 cm is **12.5 cm**.