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by SoCan » Wed Jun 01, 2011 3:07 pm
If area of larger square is 25 and is 9 times larger than the smaller square, then the area of the smaller square is 25/9. To get the length of the side, take the square root = 5/3.

Or, because the area is the square of the sides, if the area is 9 times larger, you know the length of the side is 3 times longer. Length of a side of a square with area 25 = 5. Length divided by 3 = 5/3.
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by MBA.Aspirant » Wed Jun 01, 2011 3:13 pm
The ratio is between the two "shaded" squares not the original square to the small one

area of big shaded square to that of small shaded one is 9:1
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by cans » Wed Jun 01, 2011 3:37 pm
area of original square=25
hence side=5
let side of small square=a, then that of larger = 5-a
thus (5-a)^2/a^2 = 9
taking root on each side, (5-a)/a=3
=>5-a=3a =>
a=5/4
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by MBA.Aspirant » Wed Jun 01, 2011 3:39 pm
well played - thanks!
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by SoCan » Wed Jun 01, 2011 3:39 pm
MBA.Aspirant wrote:The ratio is between the two "shaded" squares not the original square to the small one

area of big shaded square to that of small shaded one is 9:1
Yikes - didn't read the question very closely
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by cans » Wed Jun 01, 2011 3:43 pm
IMO B
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by SoCan » Wed Jun 01, 2011 3:55 pm
cans wrote:area of original square=25
hence side=5
let side of small square=a, then that of larger = 5-a
thus (5-a)^2/a^2 = 9
taking root on each side, (5-a)/a=3
=>5-a=3a =>
a=5/4
Now that I've read it properly.

Another way to look at it:

Since larger square area is 9 times that of the smaller square, it's length is 3 times that of the smaller square. Let length of side of smaller square = x, then length of side of larger square = 3x

Area of ABCD = 25, so length is 5

Length of side of ABCD = length of smaller square + length of larger square
5 = x + 3x
5= 4x
x=5/4
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by smackmartine » Wed Jun 01, 2011 8:21 pm
IMO E

let L = side of larger sq
and x = side of the smaller sq

also length of largest sq = sqrt(25) = 5 = x+L ---I


also L^2 = 9x^2
L=3x
Substituting value of L in statement I

x+3x = 5
4x=5
x=5/4
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by GMATGuruNY » Thu Jun 02, 2011 3:15 am
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?

A. 3/4
B. 5/4
C. 6/5
D. 4/3
E. 5/3
We can plug in the answers, which represent the length of one side of the smaller square.
On the GMAT, the answers likely would be listed in ascending order: 3/4, 6/5, 5/4, 4/3, 5/3.

Middle answer choice: 5/4
Since side of ABCD = 5, side of the larger shaded square = 5 - 5/4 = 15/4.
The denominators of the two lengths (5/4 and 15/4) are the same.
To compare the areas of the two squares, we need to compare only the squares of the numerators:
Bigger area:smaller area = (15^2)/(5^2) = (15/5)^2 = 9.
Success!

The correct answer is B.
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by aftableo2006 » Sun Jun 05, 2011 11:41 pm
the side of the smaller square is 5/4
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by TuanNguyen87 » Mon Jun 06, 2011 12:22 am
Because the area of ABCD is 25, so each side is 5.
Then call the larger sides are a; the smaller sides are b
And call x is the area of the smaller one => the area of the larger is 9x
Therefore, we have: a^2= 9x => a
b^2= x => b
=> a + b= 5 => we have x => finally, we figure out b= 5/4

IMO B
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by sunilramu » Mon Jun 06, 2011 7:01 am
Let the length of the small side be x.

then, x + 3x = 5 => x = 5/4
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