Answer:
Step-by-step explanation:
To solve for the side length \( x \) of the square park, we start with the equation given:
\[ x^2 + 32,500 = 76,600 \]
First, subtract 32,500 from both sides to isolate \( x^2 \):
\[ x^2 = 76,600 - 32,500 \]
\[ x^2 = 44,100 \]
Next, take the square root of both sides to solve for \( x \):
\[ x = \sqrt{44,100} \]
Calculating the square root of 44,100:
\[ x = 210 \]
Therefore, the side length \( x \) of the square park is \( \boxed{210} \) meters.
To verify:
Calculate \( x^2 \) and add 32,500 to check if it equals 76,600:
\[ 210^2 = 44,100 \]
\[ 44,100 + 32,500 = 76,600 \]
The calculations confirm that \( x = 210 \) meters is correct. Thus, the side length of the square park is \( \boxed{210} \) meters.
