SOLUTION
The diagram below would help
Because of the tangents, the side I place strokes are equal
So
From side 14.7, the part above the point is 6.7 due to tangent
The other side becomes
This make the similar stroke part to be 8 as well.
The base of the triangle becomes
Hence the perimeter becomes
Hence the answer is 44.3
Note that the polygon here is the triangle