Final answer:
The corresponding side of the 6 cm side in polygon S in the similar polygon R is 12 cm because the ratio of their perimeters is 2:1. The correct answer is option B.
Step-by-step explanation:
Polygon similarity refers to the relationship between two polygons that have the same shape but may differ in size. Similar polygons have corresponding angles that are equal and corresponding sides that are in proportion.
Two polygons are similar if:
Corresponding Angles are Congruent: The angles of one polygon correspond to the angles of the other, and these corresponding angles are equal.
Corresponding Sides are Proportional: The ratios of the lengths of corresponding sides are equal. In other words, if you take any two corresponding sides from each polygon and form a ratio, this ratio will be the same for all pairs of corresponding sides.
The student's question is about finding the length of a side of a polygon that is similar to another polygon with known dimensions. When two polygons are similar, their corresponding sides are proportional. The perimeter of polygon R is 72 cm, and the perimeter of polygon S is 36 cm, which gives us a ratio of 2:1 (72 cm/36 cm). If a side of polygon S is 6 cm, then the corresponding side in polygon R, being twice as long because of the 2:1 ratio, would be 12 cm.