You have not listed the possible lengths, but we can eliminate some integers: 1 through 5.
Let x be the length of side PR
16 + x is the perimeter of triangle PQR
Triangle STU is equilateral so let its sides be Y and Y must be an integer.
16 + x = 3Y
x = 3Y -16
Y must therefore be 6 or larger because a negative length does not make sense.