Final answer:
To find the corresponding side length in Figure B with a perimeter of 84 inches, we calculate the scale factor between the perimeters and multiply the known side length from Figure A by this scale factor, resulting in a corresponding side length of 7 inches for Figure B.
Step-by-step explanation:
The subject of the student's question involves understanding the relationship between perimeters of similar geometric figures and finding corresponding side lengths given this relationship.
Specifically, if Figure A has a perimeter of 60 inches and a known side length of 5 inches, we can use this information to determine a corresponding side length in Figure B, which has a perimeter of 84 inches. The student is essentially asked to apply notions of scale factor and proportions to solve the problem.
To find the missing corresponding side length of Figure B, we first determine the scale factor between the two figures' perimeters. Since figure B's perimeter is 84 and figure A's is 60, we divide the perimeters to find the scale factor:
Scale factor = Perimeter of B / Perimeter of A = 84 inches / 60 inches = 1.4.
Now that we know each side of Figure B is 1.4 times longer than the corresponding side of Figure A, we can find the length of the missing side in Figure B by multiplying the known side length from Figure A by the scale factor:
Missing side of B = Known side of A * Scale factor = 5 inches * 1.4 = 7 inches.
Therefore, the corresponding side length of Figure B is 7 inches.