Square A has side lengths that are 166 times the side lengths of square B. The

The correct answer is $\mathrm{27,556}$. The area of a square is $s^2$, where $s$ is the side length of the square. Let $x$ represent the length of each side of square B. Substituting $x$ for $s$ in $s^2$ yields $x^2$. It follows that the area of square B is $x^2$. It’s given that square A has side lengths that are $166$ times the side lengths of square B. Since $x$ represents the length of each side of square B, the length of each side of square A can be represented by the expression $166x$. It follows that the area of square A is ${\left(166x\right)}^2$, or $\mathrm{27,556}{x}^2$. It’s given that the area of square A is $k$ times the area of square B. Since the area of square A is equal to $\mathrm{27,556}{x}^2$, and the area of square B is equal to $x^2$, an equation representing the given statement is $\mathrm{27,556}{x}^2=k{x}^2$. Since $x$ represents the length of each side of square B, the value of $x$ must be positive. Therefore, the value of $x^2$ is also positive, so it does not equal $0$. Dividing by $x^2$ on both sides of the equation $\mathrm{27,556}{x}^2=k{x}^2$ yields $\mathrm{27,556}=k$. Therefore, the value of $k$ is $\mathrm{27,556}$.