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