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

Question

https://gmatclub.com/forum/download/file.php?id=25995 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 . 4squaresinasquare_text.PNG

Bunuel · Accepted Answer

MAGOOSH OFFICIAL SOLUTION: 4squaresinasquare_text(1).png

peachfuzz · Answer

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

EMPOWERgmatRichC · Answer

Hi Bunuel,

Should this question include a picture?

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

Bunuel · Answer

Added the image. Thank you.

camlan1990 · Answer

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

tomlui2010 · Answer

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

PareshGmat · Answer

If the area of square ABCD = 25, then each side = 5

Attachment:

4squaresinasquare_text.PNG [ 2.28 KiB | Viewed 22972 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

CounterSniper · Answer

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

spetznaz · Answer

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 !

bumpbot · Answer

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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

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