Problem Solving

In the figure shown, two identical squares are inscribed in the rectangle. If the perimeter of the
rectangle is 18*square root 2, then what is the perimeter of each square?
A. 8*square root 2
B. 12
C. 12*square root 2
D. 16
E. 18

OA – B

The perimeter of the rectangle will be 2(length + width) = 18*sqrt(2). This means that you get length + width = 9sqrt(2).

Now look at the picture and try to figure out what is length and width of rectangle in terms of x, with x = side of square.

As you can plainly see, the length will be two times the diagonal of the square, while the width will be equal to the diagonal of the square. In terms of x, the diagonal will be x*sqrt(2) (since the diagonal of a square is always equal to side of the square times sqrt(2)).

This means that you get:
length = 2*x*sqrt(2)
width = x*sqrt(2)
--------------------
3*x*sqrt(2) = 9*sqrt(2).
x = 3.

Since the side of a rectangle is 3, then the perimeter will be 4x = 12.

The perimeter of the rectangle can be equally separated into 12 pieces
Each piece = 18*sqrt(2)/12 = (3/2)*sqrt(2)

So, X = (3/2)*sqrt(2) * sqrt(2) = 3


The perimeter of the square is 3*4 = 12

DanaJ wrote:The perimeter of the rectangle will be 2(length + width) = 18*sqrt(2). This means that you get length + width = 9sqrt(2).

Now look at the picture and try to figure out what is length and width of rectangle in terms of x, with x = side of square.

As you can plainly see, the length will be two times the diagonal of the square, while the width will be equal to the diagonal of the square. In terms of x, the diagonal will be x*sqrt(2) (since the diagonal of a square is always equal to side of the square times sqrt(2)).

This means that you get:
length = 2*x*sqrt(2)
width = x*sqrt(2)
--------------------
3*x*sqrt(2) = 9*sqrt(2).
x = 3.

Since the side of a rectangle is 3, then the perimeter will be 4x = 12.

I am sorry i failed to understand your explanation.Could you please help me out with a detailed explanation...

CookieNet wrote:The perimeter of the rectangle can be equally separated into 12 pieces
Each piece = 18*sqrt(2)/12 = (3/2)*sqrt(2)

So, X = (3/2)*sqrt(2) * sqrt(2) = 3


The perimeter of the square is 3*4 = 12

I like this kind of explanation.
but why are you multiplying 3/2 * sq rt 2 with sq rt 2????

what is the sq rt 2 in this case ?

bhumika.k.shah wrote: I am sorry i failed to understand your explanation.Could you please help me out with a detailed explanation...

I think I can't go into more detail that I already have. If you can point out a specific issue you're having with the explanation, I'd be happy to help!

reply by manish8109
i found it really helpfull.....
read carefully pls if u really want to understand question...


If perimeter of rectangle= 18sqrt(2)
=> 2(a+b) = 18sqrt(2)
=> a+b=9sqrt(2) where a= length & b=breadth

Square side=s

Consider 1st square,

Diagonal=s* sqrt(2)=b(Breadth)

Consider 1st & 2nd square

diagonal 1+ diagonal2= 2s*sqrt(2)=a(Length)

=> 3s*sqrt(2)= 9 sqrt(2)
=> 3s=9
=> s=3

permeter of square=4*s=4*3=12 Ans(B)

Here is how I tackled this one.