A rectangle with a perimeter of 48 units is the image of a rectangle that was dilated by a scale factor of start fraction 3/2 Find the perimeter of the preimage, the original rectangle, before its dilation. Round your answer to the nearest tenth, if necessary.
Let the original rectangle have a length of L units and a width of W units.
Perimeter of the preimage = 2L + 2W
Given that the image (dilated rectangle) has a perimeter of 48 units, and it was dilated by a scale factor of 3/2:
Perimeter of the dilated rectangle = 48 units
Perimeter of the original rectangle = Perimeter of the dilated rectangle / scale factor
= 48 / (3/2)
= 48 * 2/3
= 32 units
So, the perimeter of the original rectangle is 32 units.