Question

Could someone help me please

Answer 1

To find the ratio of the areas, we are obviously going to first need to find the areas of the inner and outer squares. The outer square has a side length of
`a` because we are
`a` units away from 0 on the x-axis. Thus, the area of the outer square is
`a^2`.

We can see that a right triangle is formed by part of the x-axis, part of the y-axis, and the side of the inner square. Thus, we can find the length of the inner square through the Pythagorean Theorem, which is
`a^2 + b^2 = c^2`, where
`a` and
`b` are the legs of the right triangle and
`c` is the hypotenuse. The lengths of the legs of the right triangle in the picture are
`(a - b)` and
`b`. We can use the Pythagorean Theorem to find the other side length.

`(a - b)^2 + b^2 = c^2`

`c = √((a - b)^2 + b^2)`

We have now found that the side length of the inner square is
`√((a -b)^2 + b^2)`. Thus, the area of the inner square is
`(a - b)^2 + b^2`.

Using the two areas we just found, we can say that the ratio of the area of the inner square to the area of the outer square is
`((a - b)^2 + b^2)/(a^2)`, or choice A.