Each side of the square measures Convince Me! Why are there two possible solutions to the equation \( s^{2}=100 \) ? Explain why only one of the solutions is valid in this situation.

1. The equation given is \( s^2 = 100 \). To solve for \( s \), we take the square root of both sides: \[ s = \sqrt{100} \quad \text{or} \quad s = -\sqrt{100} \] 2. This yields two potential solutions: \[ s = 10 \quad \text{or} \quad s = -10 \] 3. Although both \( s = 10 \) and \( s = -10 \) satisfy the equation \( s^2 = 100 \) mathematically, in the context of a square’s side length, only non-negative values are physically meaningful because a length cannot be negative. 4. Therefore, while there are two solutions to the equation, only \( s = 10 \) is valid when representing the side length of a square.