A square garden has sides of 8ft8\operatorname{ft}. The gardener reduces each side by 1ft1\operatorname{ft} to make space for a pathway. What is the percent decrease in the perimeter of the garden?

Percent decrease = 12.5 % 12.5\% 12.5%

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

In this problem, we have a square garden whose sides are each eight feet long. The gardener wants to reduce each side by one foot to make space for a pathway. What is the percent decrease in the perimeter of the garden? So to help us understand this problem, let's draw a picture. So we have a square shaped garden whose original side lengths are each eight feet. The gardener wants to reduce the size of this garden to make way for a pathway. So our new garden is going to be a slightly smaller square, and one foot less than eight feet is seven feet. So the side lengths of this new garden will be seven feet each. We want to find the percent decrease. Now, remember percent change is calculated by finding our change in amount and dividing by our original amount. So first, let's identify our old perimeter and our new perimeter. Our old perimeter would be eight plus eight plus eight plus eight, which equals 32 feet. And our new perimeter will be seven plus seven, plus seven, plus seven, which equals 28 feet. To find our change in perimeter, we need to do new minus old. So we have twenty eight minuteus 32 equals negative four. So that's our change in amount. And then we're going to take that change in amount and divide by our original amount of 32 to find our percent change. We get negative 0.125, which as a percent is negative 12.5%. So we can say that the perimeter of the garden changed negative 12.5%. This question asks for the percent decrease. So to word our final answer, we're going to say our percent decrease was 12.5. Because remember, when we word it this way, we can drop the negative from the percent value, because the word decrease implies that the percent is negative.

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

Percent decrease = 12.5 % 12.5\% 12.5%

Percent decrease = 0.125 % 0.125\% 0.125%

Percent decrease = 62.5 % 62.5\% 62.5%

Percent decrease = 6.25 % 6.25\% 6.25%

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Intermediate Algebra

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Multiple Choice

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

Percent decrease = $0.125\%$

Percent decrease = $62.5\%$

Percent decrease = $6.25\%$

Percent decrease = $12.5\%$

Verified step by step guidance

Identify the original perimeter of the square garden. Since each side is 8 feet, use the formula for the perimeter of a square: $P = 4 \times \text{side}$. So, the original perimeter is \$4 \times 8$ feet.

Determine the new side length after the gardener reduces each side by 1 foot. Calculate the new side length as \$8 - 1$ feet.

Calculate the new perimeter using the reduced side length with the same perimeter formula: $P_{new} = 4 \times (8 - 1)$ feet.

Find the decrease in perimeter by subtracting the new perimeter from the original perimeter: $\Delta P = P - P_{new}$.

Calculate the percent decrease in perimeter using the formula: $\text{Percent decrease} = \left( \frac{\Delta P}{P} \right) \times 100\%$.

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