To find the dimensions of the original lawn, we start with the equation given:
\[ (x - 8)^2 = 144 \]
To solve for \(x\), we first take the square root of both sides:
\[ x - 8 = \sqrt{144} \]
Since \(\sqrt{144} = 12\), we have two cases to consider (positive and negative):
- \(x - 8 = 12\)
- \(x - 8 = -12\)
Case 1:
\[ x - 8 = 12 \] \[ x = 12 + 8 = 20 \]
Case 2:
\[ x - 8 = -12 \] \[ x = -12 + 8 = -4 \]
Since a side length cannot be negative, we discard Case 2. Thus, \(x = 20\).
Since \(x\) represents the side length of the original lawn, the dimensions of the original lawn are:
\[ 20 \text{ feet} , \text{by} , 20 \text{ feet} \]
Therefore, the answer is:
20 feet by 20 feet