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In the figure, the perimeter of the inscribed square is 8. What is the

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Bunuel
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In the figure, the perimeter of the inscribed square is 8. What is the [#permalink] New post   26 Jan 2022, 07:15
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In the figure, the perimeter of the inscribed square is 8. What is the are of the outside square?

A) 4√2
B) 8
C) 8√2
D) 12
E) 16

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B
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Re: In the figure, the perimeter of the inscribed square is 8. What is the [#permalink] New post   26 Jan 2022, 07:26
Bunuel wrote:

In the figure, the perimeter of the inscribed square is 8. What is the are of the outside square?

A) 4√2
B) 8
C) 8√2
D) 12
E) 16

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Attachment:
1.PNG


inscribed square each side is 2 & digonal is 2√2 which will be the side of the outside square ; so its area
(2√2)^2 ; 8
option B
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Re: In the figure, the perimeter of the inscribed square is 8. What is the [#permalink] New post   31 Jan 2022, 09:05
Let:

x = side of inscribed square

From the perimeter we can get the sides of the inscribed square.

Perimeter = 4x
8 = 4x
x = 2

The inscribed square forms right angled triangles with the outside circle where, x^2 = a^2 + a^2 (eq.1).

We know that area of square = side squared.
We can also see that side = 2a.

==> Area = (2a)^2 = 4a^2 (eq.2).

Lets refer to eq.1. Which simplifies to:

x^2 = a^2 + a^2
x^2 = 2a^2
4 = 2a^2

Now plug this into eq.2:

4a^2 = 2 * 2a^2 = 2 * 4 = 8

===> B
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Re: In the figure, the perimeter of the inscribed square is 8. What is the [#permalink] New post   31 Jan 2022, 09:18
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If you draw a horizontal line and vertical line through the center of the big square, you can immediately see that the smaller square takes up half the area of the big square. Since the smaller square has perimeter of 8, and thus has sides of length 2, its area is 4, so the big square's area is twice that, or 8.
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Re: In the figure, the perimeter of the inscribed square is 8. What is the [#permalink]
31 Jan 2022, 09:18
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