The length of a side of a square is 5x+2 units. Assuming the perimeter is 48 units, what is the area of the square?

This question is actually giving you too much information. You don't even need to find out what x is.

A square by definition has 4 equal sides. Perimeter means the sum of the length of all sides. Therefore, you know that the length of one side of the square will be equal to the perimeter divided by 4, or 48 divided by 4, or 12.

The area of a square is found by squaring the length of one side, or 12^2, which equals 144.