The area \( A \) of a square with side length \( x \) inches is given by the formula:
\[ A = x^2 \]
We want to represent the condition that the area is no more than 121 square inches. This can be expressed as:
\[ x^2 \leq 121 \]
Thus, the quadratic inequality that represents the area of the square being no more than 121 square inches is:
\[ x^2 \leq 121 \]