700 level math question

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san2009: Master | Next Rank: 500 Posts; Posts: 171; Joined: Fri Apr 16, 2010 1:02 am; Thanked: 1 times

by san2009 » Mon Jun 07, 2010 9:29 am

In the figure shown above, two identical squares are inscribed in the rectangle. If the perimeter of the rectangle is 18 by squareroot2, then what is the perimeter of each square?
(A)8 by squareroot2
(B)12
(C)12 by squareroot2
(D)16
(E)18

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liferocks: Legendary Member; Posts: 576; Joined: Sat Mar 13, 2010 8:31 pmFollowed by: 1 member; Thanked: 97 times

by liferocks » Mon Jun 07, 2010 9:33 am

Diagonal of each square is 18/(2*V2) or 9/V2

if side of the square is a diagonal will be aV2
so aV2 =9/V2 or a=9/2

hence perimeter of each square=4* 9/2 or 18

Ans option E

"If you don't know where you are going, any road will get you there."
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san2009: Master | Next Rank: 500 Posts; Posts: 171; Joined: Fri Apr 16, 2010 1:02 am; Thanked: 1 times

by san2009 » Mon Jun 07, 2010 9:49 am

sorry, whats V2?

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jeffreydamian: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Sat Feb 20, 2010 6:40 pm; Thanked: 1 times

by jeffreydamian » Mon Jun 07, 2010 10:30 am

shouldn't it be?

let x = side of square

L of rectangle = 2 diagonals of square = 2xsqrt2
W of rectangle = 1 diagonal of square = xsqrt2
perimeter = 2(2xsqrt2) + 2(xsqrt2)

or

18sqrt2 = 4xsqrt2 + 2xsqrt2
18sqrt2 = 6xsqrt2

x = 3

perimeter of square = 4x or 4x3 = 12?

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indiantiger: Master | Next Rank: 500 Posts; Posts: 362; Joined: Fri Oct 02, 2009 4:18 amFollowed by: 1 member; Thanked: 26 times

by indiantiger » Mon Jun 07, 2010 10:46 am

First of all 18 by sqrt(2) got me confused, I am going to take it as 18sqrt(2)

rectangle's perimeter = 2length + 2breadth ----(A)

from the figure we can see that length of rectangle = 2* diagonal of square (d)

from the figure we can see that breadth of rectangle = d

put these in (A)

we get 2(d+2d) = 6d

6d = 18*sqrt(2)
d= 3sqrt(2)

d = 2a^2 ('a' is the side of the square)

=> a^2 = 9*2 /2
a = 3

perimeter of square = 4*3 = 12 (ANSWER = B)

"Single Malt is better than Blended"

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san2009: Master | Next Rank: 500 Posts; Posts: 171; Joined: Fri Apr 16, 2010 1:02 am; Thanked: 1 times

by san2009 » Mon Jun 07, 2010 11:53 am

thanks a bunch!
i can't believe i didn't see that...sometimes studying doesn't pay.

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liferocks: Legendary Member; Posts: 576; Joined: Sat Mar 13, 2010 8:31 pmFollowed by: 1 member; Thanked: 97 times

by liferocks » Mon Jun 07, 2010 6:11 pm

jeffreydamian wrote:shouldn't it be?

let x = side of square

L of rectangle = 2 diagonals of square = 2xsqrt2
W of rectangle = 1 diagonal of square = xsqrt2
perimeter = 2(2xsqrt2) + 2(xsqrt2)

or

18sqrt2 = 4xsqrt2 + 2xsqrt2
18sqrt2 = 6xsqrt2

x = 3

perimeter of square = 4x or 4x3 = 12?

Sorry..I read the question as the breath of the rectangle in 18/V2 ...you are correct.It should be
6*aV2 =18/V2 [18 by squareroot2 and V2 is squareroot2]

in this way 4a=6..am I again making any mistake or the perimeter is 18 squareroot2? @san2009 can you please confirm.

"If you don't know where you are going, any road will get you there."
Lewis Carroll

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pverma23: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Thu Aug 20, 2015 10:32 am

by pverma23 » Thu Aug 20, 2015 10:52 am

I know this post is super old, but I tried it out today and others might too. Hope my approach - less algebraic more geometric - helps someone.

The square within the rectangle can be viewed as two special triangles put together, where the hypotenuse/diagonal of the square is root2.

The height of the rectangle is one hypotenuse long, and the length is 2 hypotenuses long, so the perimeter = 6 hypotenuses, all of which are factors of root2. The perimeter is 18root2. 18root2/6 = 3root2.

If the hypotenuse/diagonal of the square is 3*root2, then each side is 3*1 = 3 (ratios of special triangle 1:1:root2). Therefore each side = 3 and 3*4 = 12, the perimeter of the square.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Aug 20, 2015 11:13 am

san2009 wrote:In the figure shown above, two identical squares are inscribed in the rectangle. If the perimeter of the rectangle is 18 by squareroot2, then what is the perimeter of each square?
(A)8âˆš2
(B)12
(C)12âˆš2
(D)16
(E)18

Since the height of the rectangle and the diagonal of a square are the same length, let's let x = height of rectangle

Since the width of the rectangle is equal to the length of two square diagonals, then the width of the rectangle = 2x.

The area of the rectangle is 36.
So, (base)(height) = 36
(2x)(x) = 36
2xÂ²= 36
xÂ²= 18
x = âˆš18

NOTE: There's no need to simplify âˆš18 at this point (you'll see why shortly)

If the height of the rectangle is âˆš18, then the length of the red line (shown below) must equal âˆš18/(2)

Likewise, the other red line has length âˆš18/(2)

If we let y = the length of the hypotenuse, then the Pythagorean Theorem states that...

Now solve this equation for y.

If y = 3, then the perimeter of one square = (4)(3) = 12

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Fri Aug 21, 2015 7:13 pm

Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

In the figure shown above, two identical squares are inscribed in the rectangle. If the perimeter of the rectangle is 18 by squareroot2, then what is the perimeter of each square?
(A)8 by squareroot2
(B)12
(C)12 by squareroot2
(D)16
(E)18

==> Since the rectangle is consists of two big squares next to each other with each side of the square is a, then 6a=18sqrt2, a=3sqrt2. Then the diagonal side of the square is 6(right angled triangle with angles of 45 degrees has ratio of 1:1:sqrt2). Then each side of the small square inside has length of 3, and since the problem asks for the perimeter of the small square, 4*3 = 12, therefore the answer is B

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ArefinM: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Mon Aug 24, 2015 9:28 pm; Location: Dhaka

by ArefinM » Mon Aug 24, 2015 10:46 pm

I am bit confused. I am new. The question says the parameter is 18 by squareroot2. However, the calculation shows parameter of the rectangle in 18 into squareroot2. confused.

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