Two sides of a parallelogram are 10 cm and 15 cm. If the altiude corresponding to the side of length 15 cm is 5 cm, then what is the altitude to the side of length 10 cm ?

Options

A. 5 cm
B. 7.5 cm
C. 10 cm
D. 15 cm

Answer

To find the altitude corresponding to the side of length 10 cm in a parallelogram where the other side is 15 cm and the altitude corresponding to the side of length 15 cm is 5 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Calculate the area of the parallelogram using the base of 15 cm and its corresponding height of 5 cm.**
- Area = Base × Height
- Area = 15 cm × 5 cm = 75 cm²

2. **Use the area to find the altitude corresponding to the side of length 10 cm.**
- Let the altitude corresponding to the base of 10 cm be denoted as \( h \).
- The area can also be expressed using the base of 10 cm:
- Area = Base × Height
- Area = 10 cm × \( h \)

3. **Set the two area expressions equal to each other:**
- 75 cm² = 10 cm × \( h \)

4. **Solve for \( h \):**
- \( h = \frac{75 \text{ cm}²}{10 \text{ cm}} \)
- \( h = 7.5 \text{ cm} \)

5. **Conclusion:**
- The altitude corresponding to the side of length 10 cm is 7.5 cm.

### Final Answer:
The altitude to the side of length 10 cm is **7.5 cm**.