Question

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.

the length of each side of the original garden was (circ) feet.

the area of the original garden was (circ) feet².

Explanation:

Step1: Solve the equation \((x - 1)^2 = 25\) for \(x\)

Take the square root of both sides: \(x - 1=\pm\sqrt{25}\)
Since \(\sqrt{25} = 5\), we have \(x - 1=\pm5\)

Step2: Consider the positive solution (since side length can't be negative)

Case 1: \(x - 1 = 5\)
Add 1 to both sides: \(x=5 + 1=6\)

Case 2: \(x - 1=-5\)
Add 1 to both sides: \(x=-5 + 1=-4\) (discarded as side length can't be negative)

So, the side length of the original garden \(x = 6\) feet.

Step3: Calculate the area of the original garden

The area of a square is \(A = x^2\). Substitute \(x = 6\):
\(A=6^2 = 36\) square feet.

Answer:

The length of each side of the original garden was \(\boldsymbol{6}\) feet.
The area of the original garden was \(\boldsymbol{36}\) feet\(^2\).