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

To find the distance between the shorter sides of the parallelogram, we need to use the properties of a parallelogram.

In a parallelogram, opposite sides are equal in length and parallel. Since the adjacent sides of the parallelogram are given as 15cm and 8cm, it means that the opposite side lengths are also 15cm and 8cm.

Now, let's label the parallelogram ABCD, where AB and CD are the longer sides and AD and BC are the shorter sides.

The distance between the longer sides is 4cm, which means that the vertical distance between AB and CD is 4cm. Let's call this distance h.

To find the distance between the shorter sides, we can use the formula for the area of a parallelogram:

Area = base * height

We know that the area of a parallelogram is equal to the product of the length of a side and the corresponding height.

Applying this formula, we have:

Area = AD * h

Since the area of a parallelogram can also be calculated as the product of the base (AB) and the corresponding height (h), we can set up the following equation:

Area = AB * h

Since the area of a parallelogram is the same, we can equate the two expressions:

AD * h = AB * h

Now, let's substitute the given values:

15cm * h = 8cm * 4cm

Simplifying the equation:

15h = 32

Dividing both sides by 15:

h = 32 / 15

Therefore, the distance between the shorter sides of the parallelogram is approximately 2.133 cm (rounded to three decimal places).

If the distance is x, then we have for the area

a = 15*4 = 8x

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