SAT Question c4e5e23c: Area and Volume answer and explanation with Desmos solution

Choice A is correct. The area, $A$, of a square is given by the equation $A=s^2$, where $s$ is the length of one side of the square. Let $x$ represent the length, in feet, of one side of square N. It's given that the area of square N is $49$ square feet; therefore, it follows that $49=x^2$. It’s also given that the length of one side of square M is $6$ times the length of one side of square N. Therefore, the length of one side of square M can be represented by the expression $6x$. Substituting $6x$ for $s$ in the equation $A=s^2$ yields $A=(6x{)}^2$, or $A=36x^2$. Since $49=x^2$, substituting $49$ for $x^2$ in the equation $A=36x^2$ yields $A=36(49)$, or $A=1,764$. Therefore, the area, in square feet, of square M is $1,764$.