the longer side of a parallelogram is 54cm and the corresponding altitude is 16cm. if the altitude corresponding to the shorter side is 32cm, find the length of the shorter side.

Simply find the area in two ways:

if base is 54 and height is 16
area = 54(16)

if base is x and height is 32
area = 32x

32x = 54(16)
x = 54(16)/32 = 27

To find the length of the shorter side of the parallelogram, we can use the formula:

Area = base x height

In this case, the longer side of the parallelogram is given as 54cm, and the corresponding altitude is given as 16cm.

So, the area of the parallelogram is 54cm x 16cm = 864 square cm.

The area of a parallelogram is also equal to the product of the shorter side and its corresponding altitude. Therefore, we can write the equation as:

864 square cm = shorter side x 32cm

To find the length of the shorter side, we can rearrange the equation:

shorter side = 864 square cm / 32cm

Simplifying, we have:

shorter side = 27 cm

Therefore, the length of the shorter side of the parallelogram is 27 cm.