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# The figure above shows the dimensions of a rectangular board

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The figure above shows the dimensions of a rectangular board [#permalink]

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27 Apr 2009, 21:09
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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)
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Jan 2014, 02:04, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: Geometry........ [#permalink]

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27 Apr 2009, 23:13
I think this should be it. Perfect.
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Re: Geometry........ [#permalink]

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27 Apr 2009, 23:33
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.
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Re: Geometry [#permalink]

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19 Aug 2009, 15:56
Would anybody know if this is a GMAT question?

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

Thanks
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Re: Geometry [#permalink]

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19 Aug 2009, 16:09
I´m with C:

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

You dont need trigonometry stuff.

Regards,
-Noboru
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Re: Geometry [#permalink]

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19 Aug 2009, 16:21
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

I don't understand your approach.

Thanks a lot
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Re: Geometry [#permalink]

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20 Aug 2009, 14:05
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

I don't understand your approach.

Thanks a lot

AB=AD+DB
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
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Re: Geometry [#permalink]

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21 Aug 2009, 19:35
AB+BC=120
AB=BC+6

then
AB=63 inches

ans is C.
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Re: Geometry [#permalink]

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21 Aug 2009, 21:02
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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
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Re: Geometry [#permalink]

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25 Oct 2010, 04:59
Can I ask our math gurus to look at this one, as I don't understand the explanation quite well. Thank you.
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Re: Geometry [#permalink]

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09 Nov 2010, 11:12
nonameee wrote:
Can I ask our math gurus to look at this one, as I don't understand the explanation quite well. Thank you.

What exactly you dont understand? I will be glad to help you
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Re: Geometry [#permalink]

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09 Nov 2010, 20:20
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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 7497 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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Re: Geometry [#permalink]

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10 Nov 2010, 10:20
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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.
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Re: Geometry [#permalink]

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11 Nov 2010, 02:47
Karishma, thanks a lot. I got it.
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Re: Geometry [#permalink]

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08 Jan 2014, 23:04
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Re: The figure above shows the dimensions of a rectangular board [#permalink]

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01 Aug 2015, 08:30
Hello from the GMAT Club BumpBot!

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Re: The figure above shows the dimensions of a rectangular board [#permalink]

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24 Mar 2016, 09:47
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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Re: The figure above shows the dimensions of a rectangular board   [#permalink] 24 Mar 2016, 09:47
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# The figure above shows the dimensions of a rectangular board

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