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Sliva [168]
3 years ago
13

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

Mathematics
2 answers:
Anastasy [175]3 years ago
4 0

Answer:

\frac{(a-b)^2+b^2}{a^2}

Step-by-step explanation:

Since, By the given diagram,

The side of the inner square = Distance between the points (0,b) and (a-b,0)

=\sqrt{(a-b-0)^2+(0-b)^2}

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

Thus the area of the inner square = (side)²

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

=(a-b)^2+b^2\text{ square cm}

Now, the side of the outer square = Distance between the points (0,0) and (a,0),

=\sqrt{(a-0)^2+0^2}

=\sqrt{a^2}=a

Thus, the area of the outer square = (side)²

=a^2\text{ square cm}

Hence, the ratio of the area of the inner square to the area of the outer square

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

8090 [49]3 years ago
4 0

Answer:

I got this fraction:

frac{(a-b)^2+b^2}{a^2}

(I got the answer correct)

Hope this is helpful :)

Step-by-step explanation:

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