What is the perimeter of a parallelogram, if its area is 24 cm2 and the distances between the point of intersection of the diagonals and the sides are 2 cm and 3 cm? (added 60 points)

20 cm

The area of a parallelogram is given by the following formula:

  (1)

Where is the width and is the height of the parallelogram.

Now, let's call the point of intersection of the diagonals c. We know the distances between c and the sides are 2 cm and 3 cm, respectively, as shown in the figure attached.

From this we are able to know that the distance between c and one of the sides is the half of the width, and the distance between c and the other side is the half of the height.

This means the width of the parallelogram is:

  (2)

And its height is:

  (3)

We can prove this with the formula of the area of the parallelogram (1):

Now, the perimeter of a parallelogram is:

   (4)

Substituting the values of and in (4):

We finally get the perimeter: