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

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Math Expert
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Posts: 50002
If square ABCD has area 25, and the area of the larger shaded square i  [#permalink]

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19 Mar 2015, 06:48
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35% (medium)

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76% (02:18) correct 24% (02:35) wrong based on 175 sessions

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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 [ 1.96 KiB | Viewed 5552 times ]

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Math Expert
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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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23 Mar 2015, 05:25
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Bunuel wrote:

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 [ 16.09 KiB | Viewed 4762 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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19 Mar 2015, 09:03
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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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19 Mar 2015, 18:37
1
Hi Bunuel,

Should this question include a picture?

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Math Expert
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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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20 Mar 2015, 05:37
EMPOWERgmatRichC wrote:
Hi Bunuel,

Should this question include a picture?

GMAT assassins aren't born, they're made,
Rich

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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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20 Mar 2015, 17:51
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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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20 Mar 2015, 22:02
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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25 Mar 2015, 03:43
1
If the area of square ABCD = 25, then each side = 5

Attachment:

4squaresinasquare_text.PNG [ 2.28 KiB | Viewed 4728 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

$$x = \frac{5}{4}$$

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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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25 Jul 2018, 10:26
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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04 Aug 2018, 22:47
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, 22:47
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# If square ABCD has area 25, and the area of the larger shaded square i

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