A square with a side length of 2s 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 answer has to be 2:1
To find the area of the smaller square, we need to consider that the side length of the smaller square is half the side length of the larger square. Therefore, the side length of the smaller square is s.
The area of the larger square is (2s)^2 = 4s^2.
The area of the smaller square is s^2.
The ratio of the larger square to the area of the smaller square is 4s^2 : s^2 = 4:1.
Since s = 1/2 times the side length of the larger square (2s), the ratio simplifies to 4:1 = 2:1.
Therefore, the ratio of the larger square to the area of the smaller square is 2:1.