SAT Question 1fe41c6b: Area and Volume answer and explanation with Desmos solution

Choice D is correct. It’s given that rectangle A and rectangle B are similar. Therefore, there is a positive constant $k$ such that the length of each side of rectangle B is $k$ times the length of the corresponding side of rectangle A and the area of rectangle B is $k^2$ times the area of rectangle A. It’s also given that the area of rectangle A is $630$ square inches and that the area of rectangle B is $2,520$ square inches. It follows that $2,520=630k^2$. Dividing both sides of this equation by $630$ yields $4=k^2$, or $k^2=4$. Taking the positive square root of each side of this equation yields $k=2$. Therefore, the length of each side of rectangle B is $2$ times the length of the corresponding side of rectangle A. It follows that the perimeter of rectangle B is $2$ times the perimeter of rectangle A. Since the perimeter of rectangle A is $210$ inches, the perimeter of rectangle B is $2(210)$, or $420$, inches. Therefore, $n=420$.