The adjacent sides of a parallelogram are 15 cm and 8 cm. If the distance between thelonger sides is 4 cm, find the distance between the shorter sides.

Answer

To solve the problem step by step, let's follow the reasoning presented in the video transcript.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Length of the longer side (base) of the parallelogram, \( AB = 15 \, \text{cm} \)
- Length of the shorter side (base) of the parallelogram, \( BC = 8 \, \text{cm} \)
- Distance (height) between the longer sides, \( h_1 = 4 \, \text{cm} \)

2. **Calculate the Area of the Parallelogram Using the Longer Side:**
- The area \( A \) of a parallelogram can be calculated using the formula:
\[ A = \text{base} \times \text{height} \]
- Here, we take the longer side as the base:
\[ A = 15 \, \text{cm} \times 4 \, \text{cm} = 60 \, \text{cm}^2 \]

3. **Use the Area to Find the Distance Between the Shorter Sides:**
- We know the area remains the same regardless of which side we take as the base. Now we will use the shorter side \( BC \) as the base.
- Let \( h_2 \) be the distance between the shorter sides. Using the area formula again:
\[ A = \text{base} \times \text{height} \]
- Substituting the known values:
\[ 60 \, \text{cm}^2 = 8 \, \text{cm} \times h_2 \]

4. **Solve for \( h_2 \):**
- Rearranging the equation to find \( h_2 \):
\[ h_2 = \frac{60 \, \text{cm}^2}{8 \, \text{cm}} = 7.5 \, \text{cm} \]

5. **Conclusion:**
- The distance between the shorter sides of the parallelogram is \( 7.5 \, \text{cm} \).