A square garden has sides of $8\mathrm{ft}$. The gardener reduces each side by $1\mathrm{ft}$ to make space for a pathway. What is the percent decrease in the perimeter of the garden?

• A. Percent decrease = $0.125\%$
• B. Percent decrease = $62.5\%$
• C. Percent decrease = $6.25\%$
• D. Percent decrease = $12.5\%$

Answer: (D)

Verified step by step guidance

1. Identify the original side length of the square garden, which is given as \(8\) feet.
2. Calculate the original perimeter of the garden using the formula for the perimeter of a square: \(P = 4 \times \text{side}\). So, the original perimeter is \(4 \times 8\) feet.
3. Determine the new side length after reducing each side by \(1\) foot. The new side length is \(8 - 1\) feet.
4. Calculate the new perimeter with the reduced side length using the same perimeter formula: \(P_{new} = 4 \times (8 - 1)\) feet.
5. Find the percent decrease in the perimeter by using the formula: \(\text{Percent Decrease} = \frac{P_{original} - P_{new}}{P_{original}} \times 100\%\). Substitute the values found in previous steps to set up this expression.