Final Answer:
For the perimeter of square A (4n) to be less than the perimeter of rectangle B (2(5 + n)), the value of n must be less than 5, as per the comparison of their formulas. Therefore the correct option is c.
Step-by-step explanation:
To determine when the perimeter of square A is less than the perimeter of rectangle B, we need to compare their formulas. The perimeter of a square is given by P_square = 4n, where n is the length of one side. The perimeter of a rectangle is P_rectangle = 2(length + width), which for this case would be 2(5 + n). To find when the perimeter of square A (4n) is less than that of rectangle B (2(5 + n)), we set up the inequality 4n < 2(5 + n).
Expanding and solving for n:
4n < 10 + 2n
4n - 2n < 10
2n < 10
n < 5
The value of n must be less than 5 for the perimeter of square A to be less than the perimeter of rectangle B. This means that when the length of one side of the square is less than 5 units, the square's perimeter will be smaller than the perimeter of the given rectangle with a length of 5 and width of n.
This conclusion aligns with option c, stating n < 5, accurately representing the values for which the perimeter of square A will be less than that of rectangle B.
The comparison of the perimeters demonstrates that when n is any value less than 5, the square's total distance around its sides will be shorter than the distance around the rectangle, given the specific dimensions provided in the question. Therefore, option c correctly identifies the values of n that satisfy the condition for the square's perimeter to be less than that of the rectangle. Therefore the correct option is c.