Latest Elitmus Aptitude Question SOLUTION: A square of side x is given... joining the mid point of the sides another square is made...in this way it is continued...what will be the perimeter of the the 9th square???

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(#M40034244) ELITMUS Numerical Ability question Keep an EYE

A square of side x is given... joining the mid point of the sides another square is made...in this way it is continued...what will be the perimeter of the the 9th square???

Asked In Elitmus Sourav Chandra (10 years ago)

Unsolved Read Solution (15)

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RAKESH  (10 years ago)

area of 1st square = x^2
area of 2nd square = x^2/2 = x^2/2^1
area of 3rd square = x^/4 = x^2/2^2
area of 4th square = x^2/8 = x^2/2^3
......

area of 9th square = x^2/2^8

perimeter of 9th square = 4*side = 4* √(x^2/2^8) = 4*x/2^4 = 4*x/16 = x/4

Is this solution Helpfull? Yes (53) | No (8)  

RAKESH  (10 years ago)

area of 1st square = x^2
area of 2nd square = x^2/2 = x^2/2^1
area of 3rd square = x^/4 = x^2/2^2
area of 4th square = x^2/8 = x^2/2^3
......

area of 9th square = x^2/2^8

perimeter of 9th square = 4* √(x^2/2^8) = 4*(x/2)^4 = 4*x/16 = x/4

Is this solution Helpfull? Yes (7) | No   

arpit jain  (10 years ago)

since 2nd square made by joining the mid points of 1st square results sides = x/2sqrt(2)..similarly 3rd square have side x/2..then 5th as x/4..7th as..x/8..and 9th square as x/16.
Hence perimeter of 9th square is 4*x/16 = x/4 ans

Is this solution Helpfull? Yes (3) | No (2)  

Ann Theressa  (10 years ago)

Area of a square joining the midpoints of another square is half the area of original square.
ie area of 2nd square = x^2/2
area of nth square = x^2/2^(n-1)
similarly area of 9th square = x^2/2^8
= x^2/256
====> side of 9th square = x/16
perimeter = 4*side = 4*x/16 = x/4

Is this solution Helpfull? Yes (3) | No   

rohit gupta  (10 years ago)

p1- 4a (side be a the perimeter = a+a+a+a =4a)
p2- 2a (side be a the perimeter = a/2+a/2+a/2+a/2 =2a) so on..
p3- a
p4- a/2
p5- a/4
p6- a/8
p7- a/16
p8- a/32
p9- a/64

Is this solution Helpfull? Yes (3) | No (7)  

AVIJIT  (10 years ago)

in the qtn the side was 5 cm.
1st square-----------> 5 cm
2nd square----------->5/root(2)
3rd square-----------> 5/root(2)*root(2)
.
.
so on.
n times---- 5/(root(2))^n-1
here n=9
so 9th square's side will be 5/root(2)^8=5/16
perimeter=4*5/16=5/4

Is this solution Helpfull? Yes (2) | No   

komal pandhariwal  (10 years ago)

1 sq side = x
2 sq side = x/2
3 sq side = x/4
Similarly 9th sq side = x/(2^8)

So perimeter is 4*x/(2^8)= x/64

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SUDHIR SHARMA  (10 years ago)

If x is the side of the outer Square then its Perimeter will be 4x
Now ,another square is made using the mid points off all the four sides
then each side of the inner Square will be x/sqrt(2).

Therefore its Perimeter will be 8*sqrt(2)*x

Similiarly, 3rd Square will have Perimeter 2x
4th will have 4*sqrt(2)*x
.
.
.
.
9th Square will have Perimeter x/4

Is this solution Helpfull? Yes (1) | No   

Satanik Hudati  (10 years ago)

Answer: x/4sqrt(2)

Since a square is made by joining the mid points, therefore diagonal of the new square thus formed is equal to the side of the mother square(draw the fig to understand). Since, a diagonal is given by length*sqrt(2)and length is "x", diagonal of the new square is "x".
let the length of each side of new square be a1
then, a1=x/sqrt(2)
Again, a2=x/2
a3=x/2sqrt(2)
a4=x/4
.
.
.
a9=x/16sqrt(2)
Thus, each side of 9th square is x/16sqrt(2)

Now, perimeter of 9th square is x/4sqrt(2)

Thank you.

Is this solution Helpfull? Yes (1) | No (4)  

SUNIL KUMAR  (10 years ago)

all are doing
perimeter =4*area
its 4*side i think...

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juli  (10 years ago)

x/4 is the ans

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SUNIL KUMAR  (10 years ago)

komal and rohit are true .. i think.

Is this solution Helpfull? Yes | No (2)  

prasann kumar jha  (10 years ago)

it is given that the square is side of x
so side of 1st sqr= x
2nd= x/2
3rd= x/4
...

9th x/256
so side of 9th square is x/256
hence perimeter is= 4*x/256= x/64 ....

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Shreesh Tripathi  (10 years ago)

x/64
becoz perimeter is 4*side not 4*area

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sourav tripathi  (10 years ago)

side of 1st square = 6
side of 2nd square = 3*2^(1/2)
like that it forms a GP.
6,3root(2),1.5.......upto 9th term.
9th term = 0.34
perimeter of 9th square = 4*0.34 = 1.38 ans

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