Elementary Geometry for College Students (6th Edition)

For parallelogram ABCD to have perpendicular diagonals, then parallelogram ABCD is actually a rhombus. Since ABCD is a rhombus, then the diagonals also bisect each other. This will create four congruent right triangles inside rhombus ABCD with leg lengths of 5 and 12. In a right triangle, if the leg lengths are 5 and 12, then the hypotenuse is 13. The hypotenuse of each right triangle is a side of rhombus ABCD. Thus, each side has lenght 13. $13\times4=52$