To find the distance between the longer side of the parallelogram, we need to use the formula for the area of a parallelogram.

Step 1: Area of the Parallelogram

The area $A$ of a parallelogram is given by:

$A = \text{base} \times \text{height}$

We know the following:

• The length of the base (the longer side) is 15 cm.
• The perpendicular height corresponding to this base is 7 cm.

So, the area of the parallelogram is:

$A = 15 \, \text{cm} \times 7 \, \text{cm} = 105 \, \text{cm}^2$

Step 2: Finding the Distance Between the Longer Sides

Now, we use the formula for the area of the parallelogram with the other pair of adjacent sides (the shorter side):

$A = \text{side} \times \text{height}$

Here:

• The side of the parallelogram is 9 cm (the shorter side).
• We need to find the perpendicular height corresponding to this side, which we'll call $h_2$.

Since the area is the same, we can set up the equation:

$105 \, \text{cm}^2 = 9 \, \text{cm} \times h_2$

Solving for $h_2$:

$h_2 = \frac{105 \, \text{cm}^2}{9 \, \text{cm}} = 11.67 \, \text{cm}$

So, the perpendicular distance between the longer sides is approximately 11.67 cm.

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Would you like more detailed explanations or have any questions about this solution?

Related Questions:

1. How does the area formula for a parallelogram apply when the sides are not perpendicular?
2. How does the choice of base affect the perpendicular height in a parallelogram?
3. What happens to the area if the height changes but the base remains the same?
4. Can the height ever exceed the length of the base in a parallelogram?
5. How would you calculate the area of a rhombus or rectangle using similar methods?

Tip: When calculating the area of a parallelogram, make sure you're using the correct base and its corresponding height (the perpendicular distance). The area is always consistent, regardless of which side you choose as the base.