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# The figure above shows four adjacent small squares, forming one large

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Math Expert
Joined: 02 Sep 2009
Posts: 59124
The figure above shows four adjacent small squares, forming one large  [#permalink]

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31 Oct 2018, 02:04
1
1
00:00

Difficulty:

35% (medium)

Question Stats:

71% (02:21) correct 29% (02:06) wrong based on 33 sessions

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The figure above shows four adjacent small squares, forming one large square. The vertices of square RSTU are midpoints of the sides of the small squares. What is the ratio of the area of RSTU to the area of the large outer square?

A. 1/2

B. 5/9

C. 7/12

D. 3/5

E. 5/8

Attachment:

phd03.png [ 9.57 KiB | Viewed 878 times ]

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Re: The figure above shows four adjacent small squares, forming one large  [#permalink]

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31 Oct 2018, 02:31
1
Bunuel wrote:

The figure above shows four adjacent small squares, forming one large square. The vertices of square RSTU are midpoints of the sides of the small squares. What is the ratio of the area of RSTU to the area of the large outer square?

A. 1/2

B. 5/9

C. 7/12

D. 3/5

E. 5/8

Attachment:
phd03.png

For the sake of dealing with easy numbers assume the bigger side of a square is 8, it creates 2 small squares that are 4 each. since the lines bisect in the middle of the the small 4/2 = 2

Now using pythagorean theorem we can find the side of the square RSTU the width is 4+2 = 6 and the height is 2

so it becomes 36 + 4 = 40

now the area of RSTU = 40

Area of bigger square = 8*8 = 64

$$\frac{40}{64}=\frac{4 * 2 * 5}{4* 2 * 8} = \frac{5}{8}$$

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Re: The figure above shows four adjacent small squares, forming one large  [#permalink]

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31 Oct 2018, 02:32
1
Let the side of the larger square be 4 units.

Attachment:

image.jpg [ 51.38 KiB | Viewed 755 times ]

The ratio of area of RSTU to outer square is $$\frac{(\sqrt 10)^2}{16}$$

$$\frac{10}{16}$$

$$\frac{5}{8}$$

OPTION : E
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Re: The figure above shows four adjacent small squares, forming one large   [#permalink] 31 Oct 2018, 02:32
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