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.

Answer 1

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area of larger square = (2s)^2 = 4s^2

For the side of the smaller square:
x^2 = s^2 + s^2
x = √2s
area of smaller is (√2s)^2 = 2s^2
so the ratio of their areas = 4s^2 : 2s^2 = 2 : 1