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A square with side length 5 has its corner at the center of a square w

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A square with side length 5 has its corner at the center of a square w  [#permalink]

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New post 16 Jun 2020, 10:11
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A square with side length 5 has its corner at the center of a square with side length 4. The two squares overlap, and the overlapping region has one side equal to 3 as shown in the diagram above. What is the area where the two squares overlap?

A. 3
B. 4
C. 5
D. 6
E. 7

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Re: A square with side length 5 has its corner at the center of a square w  [#permalink]

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New post 16 Jun 2020, 10:26
Bunuel wrote:
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A square with side length 5 has its corner at the center of a square with side length 4. The two squares overlap, and the overlapping region has one side equal to 3 as shown in the diagram above. What is the area where the two squares overlap?

A. 3
B. 4
C. 5
D. 6
E. 7

Are You Up For the Challenge: 700 Level Questions

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Screenshot 2020-06-16 at 11.54.28 PM.png [ 41.51 KiB | Viewed 455 times ]


Area of shaded region = 1/4* Area of square - x + x = 1/4 * 4*4 = 4

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Re: A square with side length 5 has its corner at the center of a square w  [#permalink]

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New post 16 Jun 2020, 20:40
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1
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In the figure, there's a typo. Correction: CD = 3-1 = 2.

Area of triangle ABC + Area of trapezoid ACDE = 0.5 * 2 * 1 + 0.5 * (2+1) * 2 = 1 + 3 = 4
Ans: 4
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Re: A square with side length 5 has its corner at the center of a square w  [#permalink]

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New post 22 Jun 2020, 20:47
Lipun wrote:
Image

In the figure, there's a typo. Correction: CD = 3-1 = 2.

Area of triangle ABC + Area of trapezoid ACDE = 0.5 * 2 * 1 + 0.5 * (2+1) * 2 = 1 + 3 = 4
Ans: 4




Hi,

Could you please tell how did you deduce DE=1

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Re: A square with side length 5 has its corner at the center of a square w  [#permalink]

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New post 23 Jun 2020, 03:47
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DrMudassir wrote:
Hi,

Could you please tell how did you deduce DE=1

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Hi DrMudassir,

Since vertex of the larger square is the center of the smaller square, therefore, the sides of the larger square will move equal distance across each corresponding side of the smaller square when rotated about the center.
Side AB has shifted a distance of BC = 1 on the side of the smaller square, so the side AE must also have shifted by a distance of 1 unit towards D.

Hope it helps!

Lipun
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Re: A square with side length 5 has its corner at the center of a square w   [#permalink] 23 Jun 2020, 03:47

A square with side length 5 has its corner at the center of a square w

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