The adjacent sides of a parallelogram are 12 cm and 9 cm. The distance between longer sides is 6 cm; the distance between shorter sides is :

1. 12 cm

2. 9 cm

3. 8 cm

4. 6 cm

Given:

The base of the parallelogram = 12 cm.

The height of the parallelogram = 6 cm.

As we know, the area of parallelogram = base x height

The area of the parallelogram using the longer side:

= 12 x 6 cm²

= 72 cm²

The base of the parallelogram = 9 cm.

Let the height of the parallelogram be b cm.

The area of the parallelogram using the shorter side:

= 9 x b cm²

Since the area is the same, we can equate both areas:

⇒ 9 x b cm² = 72 cm²

⇒ b = $\dfrac{72}{9}$ cm

⇒ b = 8 cm

Hence, option 3 is the correct option.