Answer :
To find the effect on the perimeter when the side length of the pentagon is increased, we should follow these steps:
1. Calculate the original perimeter of the pentagon.
The pentagon has five sides, and each side is originally 4 inches long. Therefore, the original perimeter (P_original) is:
P_original = side_length * number_of_sides
P_original = 4 inches * 5
P_original = 20 inches
2. Determine the new side length after the increase.
The new side length (new_side_length) is the original side length plus the increase:
new_side_length = original_side_length + increase_in_length
new_side_length = 4 inches + 1 inch
new_side_length = 5 inches
3. Calculate the new perimeter of the pentagon with the increased side length.
The new perimeter (P_new) is the new side length multiplied by the number of sides:
P_new = new_side_length * number_of_sides
P_new = 5 inches * 5
P_new = 25 inches
4. Calculate the increase in the perimeter.
The increase in the perimeter (increase_P) is the new perimeter minus the original perimeter:
increase_P = P_new - P_original
increase_P = 25 inches - 20 inches
increase_P = 5 inches
5. Finally, calculate the percent increase in the perimeter.
The percent increase (percent_increase) is the increase in the perimeter divided by the original perimeter, then multiplied by 100 to convert it to a percentage:
percent_increase = (increase_P / P_original) * 100
percent_increase = (5 inches / 20 inches) * 100
percent_increase = 0.25 * 100
percent_increase = 25%
So, the effect on the perimeter of the pentagon when the side length is increased by 1 inch is that the perimeter increases by 25%.
