Question 168190
There seems to be an error on the problem as it is written if AB is the long side and it is 5 shorter than the short side.

The general idea is to draw the parallelogram first and label all the vertices. Define the length of the short side to be x inches long so write x alongside each of the two shorter sides. The longer side is 5 inches longer than a short side so it will be x + 5 inches long. Mark in the lengths of the two long sides.

To find the perimeter of the shape add up each of the sides. This will give x + (x + 5) + x + (x + 5) which you already know must equal 48.
{{{ x + (x + 5) + x + (x + 5) = 48}}}
{{{ x + x + 5 + x + x + 5 = 48}}}
{{{ 4x + 10 = 48}}}
{{{ 4x = 38}}}
{{{ x = 9.5}}}
This means that the short sides are 9.5 inches long and the longer sides are 5 inches longer ie 14.5 inches. Check to make sure that the sides give a total perimeter of 48 inches.