Two squares are drawn. The larger Square has area of 400 in.². The area of the two squares have a ratio of 1 to 4. What is the side length S of the smaller square?

The first thing we must do in this case is to find the area of the smallest square.
 For this, we use the following relationship:
 A1 / A2 = 4/1
 Substituting:
 400 / A2 = 4/1
 From here, we clear A2:
 A2 = (1/4) * (400)
 A2 = 100 in ^ 2
 We now look for the side of the small square, we use the following relationship:
 A = S ^ 2
 We cleared S:
 S = root (A)
 S = root (100)
 S = 10 in
 Answer:
 the side length S of the smaller square is:
 S = 10 in