A regular pentagon has a side length of 4 inches. If the side length is
increased by 1 inch, what is the effect on the perimeter of the
pentagon?
It increases by 20%.
It increases by 25%
It increases by 50%
It increases by 12.5%.
3 of 5 QUESTION



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%.