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If square ABCD has area 25, and the area of the larger shaded square i

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If square ABCD has area 25, and the area of the larger shaded square i  [#permalink]

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New post 19 Mar 2015, 05:48
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If square ABCD has area 25, and the area of the larger shaded square is 9 times the area of the smaller shaded square, what is the length of one side of the smaller shaded square? Note: Figure not drawn to scale

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

Kudos for a correct solution.


Attachment:
4squaresinasquare_text.PNG
4squaresinasquare_text.PNG [ 1.96 KiB | Viewed 5899 times ]

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Re: If square ABCD has area 25, and the area of the larger shaded square i  [#permalink]

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New post 23 Mar 2015, 04:25
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Bunuel wrote:
Image
If square ABCD has area 25, and the area of the larger shaded square is 9 times the area of the smaller shaded square, what is the length of one side of the smaller shaded square? Note: Figure not drawn to scale

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

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:
Attachment:
4squaresinasquare_text(1).png
4squaresinasquare_text(1).png [ 16.09 KiB | Viewed 5062 times ]

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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: If square ABCD has area 25, and the area of the larger shaded square i  [#permalink]

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New post 19 Mar 2015, 08:03
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Let x be the side of the smaller shaded square, and y the side of the larger shaded square

x + y = sqrt (25)
x + y = 5

y^2 = 9x^2
y = 3x

x + 3x = 5
x = 5/4
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Re: If square ABCD has area 25, and the area of the larger shaded square i  [#permalink]

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New post 19 Mar 2015, 17:37
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Hi Bunuel,

Should this question include a picture?

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Re: If square ABCD has area 25, and the area of the larger shaded square i  [#permalink]

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New post 20 Mar 2015, 04:37
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Re: If square ABCD has area 25, and the area of the larger shaded square i  [#permalink]

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New post 20 Mar 2015, 16:51
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The area of larger shaded square = 9*The area of smaller shaded square => The side of larger shaded = 3*The side of larger shaded => The side of smaller shaded square = 1/4 * side of ABCD.

Area of ABCD = 25 => Its side = 5 => The side of smaller shaded square = 1/4*5=5/4
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Re: If square ABCD has area 25, and the area of the larger shaded square i  [#permalink]

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New post 20 Mar 2015, 21:02
1
Area in the ratio => 9:1
Sides then will be in the ratio => 3:1
Diagonals hence will be in the ratio => 3:1
Diagonal of the bigger square is 5 * \sqrt{2}
Hence, Diagonal of the shaded smaller square, (side * \sqrt{2}) => 1/4*(5 * \sqrt{2})
Therefore, side of the shaded smaller square => 5/4
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Re: If square ABCD has area 25, and the area of the larger shaded square i  [#permalink]

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New post 25 Mar 2015, 02:43
1
If the area of square ABCD = 25, then each side = 5

Attachment:
4squaresinasquare_text.PNG
4squaresinasquare_text.PNG [ 2.28 KiB | Viewed 5024 times ]


Say side of small square = x

Given that \(9x^2 = (5-x)^2\)

\(8x^2 + 10x - 25 = 0\)

\(8x^2 + 20x - 10x - 25 = 0\)

4x(2x + 5) - 5(2x+5) = 0

(4x-5)(2x+5) = 0

\(x = \frac{5}{4}\)

Answer = B
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Re: If square ABCD has area 25, and the area of the larger shaded square i  [#permalink]

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New post 25 Jul 2018, 09:26
Bunuel wrote:
Attachment:
4squaresinasquare_text.PNG
If square ABCD has area 25, and the area of the larger shaded square is 9 times the area of the smaller shaded square, what is the length of one side of the smaller shaded square? Note: Figure not drawn to scale

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

Kudos for a correct solution.


let a and A be the sides of smaller and larger square.
area of smaller square = a^2
of larger square=A^2
ATQ !!
A^2=9a^2
A=3a
A+a=5
4a=5
a=5/4
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Re: If square ABCD has area 25, and the area of the larger shaded square i  [#permalink]

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New post 04 Aug 2018, 21:47
Let the length of the smaller side be x. As per the question, 9*x*x=(5-x)*(5-x). x comes to 5/4. Option B it is !
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Re: If square ABCD has area 25, and the area of the larger shaded square i &nbs [#permalink] 04 Aug 2018, 21:47
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