A square with a side length of 4s cm has a smaller square inscribed. The vertices of the smaller square are at the midpoints of the sides of the larger square. What is the ratio of the larger square to the area of the smaller square? Express your answer in simplest form
The area of the larger square with side length 4s cm is (4s)^2 = 16s^2 cm^2.
The side length of the smaller square can be found using the Pythagorean theorem. Since the vertices of the smaller square are at the midpoints of the sides of the larger square, the side length of the smaller square is 2s cm.
Therefore, the area of the smaller square is (2s)^2 = 4s^2 cm^2.
The ratio of the larger square to the area of the smaller square is 16s^2 cm^2 / 4s^2 cm^2 = 16 / 4 = 4.
So, the ratio of the larger square to the area of the smaller square is 4:1.