A square has an area that is less than \( 100 \mathrm{~m}^{2} \). What is a reasonable range for the graph of the square's side?

To find a reasonable range for the side length of a square given that its area is less than \( 100 \mathrm{~m}^{2} \), we can follow these steps: 1. **Understand the relationship between area and side length**: The area \( A \) of a square is given by the formula: \[ A = s^2 \] where \( s \) is the length of one side of the square. 2. **Set up the inequality**: Since we know that the area is less than \( 100 \mathrm{~m}^{2} \), we can write the inequality: \[ s^2 < 100 \] 3. **Solve for \( s \)**: To find the range for \( s \), we take the square root of both sides of the inequality: \[ s < \sqrt{100} \] This simplifies to: \[ s < 10 \] 4. **Consider the non-negative side length**: Since the side length of a square cannot be negative, we also have: \[ s \geq 0 \] 5. **Combine the results**: Therefore, the reasonable range for the side length \( s \) of the square is: \[ 0 \leq s < 10 \] In conclusion, the reasonable range for the graph of the square's side length is \( [0, 10) \).