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vlada-n [284]
3 years ago
8

Could someone help me please

Mathematics
1 answer:
Harrizon [31]3 years ago
8 0

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 = \sqrt{(a - b)^2 + b^2}


We have now found that the side length of the inner square is \sqrt{(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 \dfrac{(a - b)^2 + b^2}{a^2}, or choice A.

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