Step 1: Identify Given Data

We are given the area of the square plot as $289 \text{ m}^2$. Let the side length of the square be $s$.

$\text{Area} = 289$

Step 2: Apply the Area Formula

The area of a square is calculated by squaring the length of its side: $\text{Area} = s^2$

$s^2 = 289$

Step 3: Calculate the Side Length

To find the side length $s$, take the square root of both sides: $s = \sqrt{289}$

$s = 17$

Step 4: Verify with Options

Since $17 \times 17 = 289$, the side length is $17\text{ m}$, which matches Option C.

$17 \text{ m}$