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Manager  Joined: 02 Sep 2008
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The figure above shows the dimensions of a rectangular board that is t  [#permalink]

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36 00:00

Difficulty:   95% (hard)

Question Stats: 51% (03:02) correct 49% (03:11) wrong based on 342 sessions

### HideShow timer Statistics The figure above shows the dimensions of a rectangular board that is to be cut into four identical pieces by making cuts at points A, B, and C, as indicated. If x = 45, what is the length AB ? (1 foot = 12 inches)

A. 5 ft 6 in
B. 5 ft $$3\sqrt{2}$$ in
C. 5 ft 3 in
D. 5 ft
E. 4 ft 9 in

PS15302.01

Attachment: ps4.JPG [ 33.08 KiB | Viewed 15973 times ]

Attachment: 2019-09-21_1803.png [ 16.57 KiB | Viewed 3554 times ]

Originally posted by milind1979 on 27 Apr 2009, 20:09.
Last edited by Bunuel on 21 Sep 2019, 06:04, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Veritas Prep GMAT Instructor V
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Re: The figure above shows the dimensions of a rectangular board that is t  [#permalink]

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milind1979 wrote:
Attachment:
The attachment ps4.JPG is no longer available

The length of the rectangle is 240 inches. The diagram shows you the isosceles triangle whose side will be 6 inches. From 240, if we remove 2 of these sides of 6 inches each, we will be left with 228 inches.

Attachment: Ques.jpg [ 8.15 KiB | Viewed 14576 times ]

This 228 inches has to be equally divided into 4 parts as shown by the blue arrows. Why are these parts equal? Because the question says that the four pieces are identical. So the smaller side of each piece has to be equal (Look at the blue line on the top. This should be equal to the blue lines at the bottom).

The length of each of the blue lines will be 228/4 = 57 inches.
The length of AB = 57 + 6 inches = 63 inches.
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##### General Discussion
Manager  Joined: 08 Jan 2009
Posts: 200
Re: The figure above shows the dimensions of a rectangular board that is t  [#permalink]

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Same method

We can write the length of the rectangle as 2x + 2y = 240

x + y 120 -----------1

given X = 45 degrees, we draw a line perpendicular to line AB and form a right triangle with X as one of the internal angles.

From that triangle we can write tan45 = 6/y-x

y - x = 6 ---------2

Sove both we get y = 63 inch

Done.
Manager  Joined: 22 Jul 2009
Posts: 147
Re: The figure above shows the dimensions of a rectangular board that is t  [#permalink]

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1
Would anybody know if this is a GMAT question?

I had never seen before a GMAT question requiring knowledge of trigonometry.

Thanks
Director  Joined: 16 Jul 2009
Posts: 618
Schools: CBS
WE 1: 4 years (Consulting)
Re: The figure above shows the dimensions of a rectangular board that is t  [#permalink]

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I´m with C:

AB=6inches+[(20feet-2*6inches)/4]=5,25feet=5 feet 3 inches

You dont need trigonometry stuff.

Regards,
-Noboru
Manager  Joined: 22 Jul 2009
Posts: 147
Re: The figure above shows the dimensions of a rectangular board that is t  [#permalink]

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Noboru,

Could you explain how did you come up with that equation?

I understood tkarthi4u's explanation. He used the tangent formula:
tan(x)= opposite / adjacent -> tan(45) = 6 / (y-x)
Given that tan(45)=1, then y-x=6
Together with x+y=120, y=63inches=5ft3in -> answer C

Thanks a lot
Director  Joined: 16 Jul 2009
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Re: The figure above shows the dimensions of a rectangular board that is t  [#permalink]

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powerka wrote:
Noboru,

Could you explain how did you come up with that equation?

I understood tkarthi4u's explanation. He used the tangent formula:
tan(x)= opposite / adjacent -> tan(45) = 6 / (y-x)
Given that tan(45)=1, then y-x=6
Together with x+y=120, y=63inches=5ft3in -> answer C

Thanks a lot

AD is 6 inches since x is 45 degrees.
To obtain DB you have to subtract 2*6inces (6 inches because of AD and other 6inches more because CE=AD) to the long side (20 feet) and divide by 4 since there are 4 segments like DB.
It´s quiet complicated to explain...

hope it helped
Intern  Joined: 14 Aug 2009
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Re: The figure above shows the dimensions of a rectangular board that is t  [#permalink]

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AB+BC=120
AB=BC+6

then
AB=63 inches

ans is C.
Senior Manager  Joined: 20 Mar 2008
Posts: 377
Re: The figure above shows the dimensions of a rectangular board that is t  [#permalink]

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2
qB = 10 ft.
Since x = 45, angle Ast=45, since traingle Ast is a isoseles triangle.

Therefore, At = st = 6 inches = .5 ft

Now, qA + tB = 10 - .5
We know that qa = tB since both the pieces must be identicial and rs = At & pz = qB

Therefore, qA + tB = 10 - .5
or, 2tB = 10 - .5 = 9.5
or, tB = 4.75
AB = tB + At = 4.75 + .5 = 5.25 = 5 ft 3 in.

Hence, C
Attachments ps4.JPG [ 37.06 KiB | Viewed 15415 times ]

Director  Joined: 23 Apr 2010
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Re: The figure above shows the dimensions of a rectangular board that is t  [#permalink]

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Can I ask our math gurus to look at this one, as I don't understand the explanation quite well. Thank you.
Director  Joined: 16 Jul 2009
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Re: The figure above shows the dimensions of a rectangular board that is t  [#permalink]

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nonameee wrote:
Can I ask our math gurus to look at this one, as I don't understand the explanation quite well. Thank you.

Manager  Joined: 01 Nov 2010
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Location: Zürich, Switzerland
Re: The figure above shows the dimensions of a rectangular board that is t  [#permalink]

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1
Draw a perpendicular till point P on AB to make it right isosceles triangle- With principle of 45-45-90 you get AP=6.
As Karishma told- there are 4 equal area rectangles. thus AB= AP+PB = 57+6 = 63 inches.
Director  Joined: 23 Apr 2010
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Re: The figure above shows the dimensions of a rectangular board that is t  [#permalink]

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Karishma, thanks a lot. I got it.
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Re: The figure above shows the dimensions of a rectangular board that is t  [#permalink]

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VeritasPrepKarishma wrote:
milind1979 wrote:
Attachment:
ps4.JPG

The length of the rectangle is 240 inches. The diagram shows you the isosceles triangle whose side will be 6 inches. From 240, if we remove 2 of these sides of 6 inches each, we will be left with 228 inches.

Attachment:
Ques.jpg

This 228 inches has to be equally divided into 4 parts as shown by the blue arrows. Why are these parts equal? Because the question says that the four pieces are identical. So the smaller side of each piece has to be equal (Look at the blue line on the top. This should be equal to the blue lines at the bottom).

The length of each of the blue lines will be 228/4 = 57 inches.
The length of AB = 57 + 6 inches = 63 inches.

Simply loved your explanation, short and crisp. No unnecessary formulae, simple common sense. I envy you, for the thought didn't strike me. I solved it but in a lengthy way. Thank you. It's a moment of qualia for me.
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Manager  G
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Re: The figure above shows the dimensions of a rectangular board that is t  [#permalink]

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From the diagram,we can create 2 90-45-45 triangles with base =6 inches. That gives us a length of 12 inches. We can create rectangles of base ACs as well.The length of the diagram is 20 x12 =240 inches. We will subtract 12 from it to 228 inches and we will divide it by 4 and 12 ,representing the 4 rectangles of base AC . This gives us 4 feet 9 inches. Then we add 6 to get 5 ft 3inches.
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Re: The figure above shows the dimensions of a rectangular board that is t  [#permalink]

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milind1979 wrote: The figure above shows the dimensions of a rectangular board that is to be cut into four identical pieces by making cuts at points A, B, and C, as indicated. If x = 45, what is the length AB ? (1 foot = 12 inches)

A. 5 ft 6 in
B. 5 ft $$3\sqrt{2}$$ in
C. 5 ft 3 in
D. 5 ft
E. 4 ft 9 in

PS15302.01

Attachment:
The attachment ps4.JPG is no longer available

Attachment:
The attachment 2019-09-21_1803.png is no longer available

There are 4 identical parallelograms.
From the figure, we see on each side of the rectangle we have 2 Long sides of the parallelogram and 2 small sides of the parallelogram.
From the figure, we can write,
2L+2S = 20 or L+S = 10
AB is a long side, hence we need to deduce the value of 'L'
S=10-L

From ABDE we can write L = S+AF
AFD is 45-45-90 triangle and AF = 1/2 ft
L = S+1/2
L = 10-L+(1/2)
2L = 21/2
L = 21/4
L = 5.25 ft
L = 5ft + 0.25ft = 5ft 3in
[1ft = 12in -> (1/4ft = 3in]

Attachments Capture.PNG [ 25.72 KiB | Viewed 2113 times ]

Intern  B
Joined: 17 May 2020
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Re: The figure above shows the dimensions of a rectangular board that is t  [#permalink]

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Hi Bunuel,

Do you have a better way to approach this question? Re: The figure above shows the dimensions of a rectangular board that is t   [#permalink] 02 Jun 2020, 08:48

# The figure above shows the dimensions of a rectangular board that is t  