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Could someone help me please

Could someone help me please-example-1
User TuanPM
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1 Answer

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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.

User Namgyal Brisson
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