A parallelogram has sides of 12 cm and 8 cm. If the distance between the 12 cm sides is 5 cm, find the distance between 8 cm sides.

Answer

To find the distance between the 8 cm sides of the parallelogram, we can follow these steps:

### Step 1: Understand the problem
We have a parallelogram with sides of 12 cm and 8 cm. The distance (height) between the 12 cm sides is given as 5 cm. We need to find the distance (height) between the 8 cm sides.

### Step 2: Draw the parallelogram
Let's visualize the parallelogram. We can label the sides as follows:
- Two sides of 12 cm (let's call them AB and CD)
- Two sides of 8 cm (let's call them BC and AD)

### Step 3: Calculate the area using the 12 cm sides
The area of a parallelogram can be calculated using the formula:
\[ \text{Area} = \text{Base} \times \text{Height} \]

Here, we can take the base as 12 cm and the height as 5 cm:
\[ \text{Area} = 12 \, \text{cm} \times 5 \, \text{cm} = 60 \, \text{cm}^2 \]

### Step 4: Set up the area equation for the 8 cm sides
Now, we will calculate the area using the 8 cm sides. Let the height between the 8 cm sides be \( h \):
\[ \text{Area} = 8 \, \text{cm} \times h \]

### Step 5: Equate the two area expressions
Since the area of the parallelogram remains the same regardless of which side we use as the base, we can set the two area expressions equal to each other:
\[ 12 \times 5 = 8 \times h \]
\[ 60 = 8h \]

### Step 6: Solve for \( h \)
To find \( h \), we can rearrange the equation:
\[ h = \frac{60}{8} \]
\[ h = 7.5 \, \text{cm} \]

### Conclusion
The distance between the 8 cm sides of the parallelogram is 7.5 cm.

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