Miles has a square garden in his backyard. He decides to decrease the size of the garden by 1 foot on each side in order to make a gravel border. After he completes his gravel border, the area of the new garden is 25 feet2. In the equation (x - 1)2 = 25, x represents the side measure of the original garden.

Question

The length of each side of the original garden was
feet.

The area of the original garden was
feet2.

Answer 1

To solve for the length of each side of the original garden, we start with the equation given, \((x - 1)^2 = 25\), where \(x\) is the side length of the original garden.

1. Solve for \(x\):

\[ (x - 1)^2 = 25 \]

Taking the square root of both sides, we have:

\[ x - 1 = 5 \quad \text{or} \quad x - 1 = -5 \]

From \(x - 1 = 5\):

\[ x = 6 \]

From \(x - 1 = -5\):

\[ x = -4 \quad \text{(not possible, since side length cannot be negative)} \]

So, the length of each side of the original garden is:

\[ x = 6 \text{ feet} \]

2. Calculate the area of the original garden:

The area of a square garden is calculated as \( \text{side}^2 \):

\[ \text{Area} = x^2 = 6^2 = 36 \text{ feet}^2 \]

Summary of Results:

• The length of each side of the original garden was 6 feet.
• The area of the original garden was 36 feet².