Answer:
x = 4.5 , perimeter = 52
Explanation:
two tangent segments to a circle from the same external point are congruent , then
PS = PT , that is
2x = 9 ( divide both sides by 2 )
x = 4.5
then
PS = 2x = 2 × 4.5 = 9
Also
QT = QU = 4
RU = RS = 13
the perimeter is then the sum of the segments
QU + RU + RS + PS + PT + QT
= 4 + 13 + 13 + 9 + 9 + 4
= 52