Final answer:
To find the ratio of the inner square to the outer square, use the formula for the area of a square (L²) and manipulate the algebraic expression ((a-b)²+b²)/(a²). By expanding and simplifying, you can then compare the areas of two squares.
Step-by-step explanation:
To calculate the ratio of the area of the inner square to the area of the outer square given by the expression ((a-b)²+b²)/(a²), we need to understand the square area formula and how to manipulate algebraic expressions.
The area of a square is given by the formula side length × side length, which can be written as L² where L represents the length of the side of the square. This can help us to compare areas when we are dealing with the inner and outer squares.
Now, looking at the provided ratio, the numerator can be expanded: (a - b)² + b² expands to a² - 2ab + b² + b² or a² - 2ab + 2b². Therefore, the ratio simplifies to (a² - 2ab + 2b²)/a² which simplifies further by canceling out a² and the result is 1 - 2b/a + 2b²/a². To better understand how these areas compare, you would substitute specific values for a and b.