Answer
48
Work Step by Step
The triangle in the upper left is a right triangle with a leg with a length of 3 and a hypotenuse with a length of 5. You may recognize this immediately as a 3-4-5 triangle, or you can use 3$^{2}$ + x$^{2}$ = 5$^{2}$ and solve for x.
The rectangle had a width of 16, but when rearranging the pieces into a square the triangle we previously recognized as a 3-4-5 triangle will be removed, leaving a width of 12. This being a square, all sides are the same, so 4 sides with a length of 12 adds up to a total length of 48.