What is the ratio of the area of the inner square to the area of the outer

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The area of the square is

where

x is the length side of the square

step 1

Find the area of the outer square (A_o)

we have that

substitute in the formula

step 2

Find the area of the inner square (A_i)

we know that

The length side of the inner square is equal to the hypotenuse of a right triangle

so

Applying Pythagoras theorem

Remember that

so

step 3

Find the ratio of the area of the inner square to the area of the outer

substitute the values

is this the complete