Final answer:
To find the lengths of the sides of △PQR, multiply the corresponding sides of △ABC by the scale factor 1.25. The 45° counterclockwise rotation affects orientation, not side lengths. Without the specific lengths of △ABC, we can't definitively match the lengths given to sides PQ, PR, or QR.
Step-by-step explanation:
The subject of the question is mathematics, specifically geometry dealing with similar triangles, dilations, and rotations. Given that △ABC and △PQR are similar and that △ABC is dilated by a scale factor of 1.25 to form △PQR, the lengths of the sides of △PQR can be determined by multiplying the corresponding sides of △ABC by this scale factor.
The rotation of the triangle 45° counterclockwise about point B does not change the lengths of the sides, it only changes the orientation of the triangle. Therefore, if we are given the lengths of the sides of △ABC, we simply scale those lengths by 1.25 to find the lengths of the sides of △PQR. Without knowing the specific lengths of △ABC, we cannot match the side lengths of △PQR to options (a), (b), or (c). However, the process is to multiply each side of △ABC by 1.25. If any side of △ABC had a length that when multiplied by 1.25 matches the lengths given in the options, then we would have our answer.