Answer:
36 Units.
Explanation:
In the diagram attached, K, M, P and R are points of tangency.
Theorem: Tangents to a circle from the same point are equal.
By the theorem above,
LK=LM=6 Units
NM=NP=2 Units
QP=QR=7 Units
JR=JK=3 Units
Therefore:
JL=JK+KL=3+6=9 Units
LN=LM+LN=6+2=8 Units
NQ=NP+PQ=2+7=9 Units
QJ=QR+RJ=7+3=10 Units
Therefore, the perimeter of the polygon JLNQ =9+8+9+10
=36 Units.
Note: The second diagram shows the theorem already applied.