Final answer:
The perimeter of triangle ABC remains the same after a 135-degree rotation to form triangle A'B'C', as rotation is a rigid transformation. Additional information on side lengths is required to calculate the exact perimeter.
Step-by-step explanation:
The question involves finding the perimeter of triangle ABC after it has undergone a 135-degree rotation around point S to create a new triangle A'B'C'. The perimeter of a triangle is the sum of the lengths of its three sides. To answer this question, we need additional information about the sides of the original triangle ABC. However, it appears there might be an error in the provided information, as there is no direct geometric reasoning connecting the rotation of a triangle to its perimeter without knowing the lengths of its sides or having additional properties or context.
Normally, if we know the measurements of the sides of the triangle before rotation, the perimeter will remain the same after the rotation since rotation is a rigid transformation and does not change the size or shape of geometric figures. Therefore, if the side lengths of ABC were given, we could calculate the perimeter of ABC simply by adding the lengths of sides AB, BC, and CA.