To find the length of BD

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sat Nov 30, 2013 4:19 pm

Hello,

Can you please assist with this:

In the figure above, polygon ABCDEF is equilateral and has perimeter 42. If AB is
parallel to ED, AF is parallel to BC, EF is parallel to CD, and x equals 60
degrees, what is the length of line segment BD (not shown)?

OA: [spoiler]7.sqroot(3)[/spoiler]

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Source: Beat The GMAT — Problem Solving | Sat Nov 30, 2013 4:19 pm

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sat Nov 30, 2013 5:37 pm

Hi gmmattesttaker2,

I'm going to give you a couple of hints and let you try this question again:

1) Look for "hidden" right triangles. Notice how x = 60 degrees? Think about WHERE you could find right triangles inside and OUTSIDE of the given shape.
2) Since the 6-sided shape is equilateral, what does that mean about the 6 sides?
3) Line segment BD is OUTSIDE the shape. Try drawing that into the picture, then cut that line IN HALF.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sat Nov 30, 2013 6:06 pm

[email protected] wrote:Hi gmmattesttaker2,

I'm going to give you a couple of hints and let you try this question again:

1) Look for "hidden" right triangles. Notice how x = 60 degrees? Think about WHERE you could find right triangles inside and OUTSIDE of the given shape.
2) Since the 6-sided shape is equilateral, what does that mean about the 6 sides?
3) Line segment BD is OUTSIDE the shape. Try drawing that into the picture, then cut that line IN HALF.

GMAT assassins aren't born, they're made,
Rich

Hi Rich,

I was wondering if length BD is also included in the perimeter of ABCDEF and similarly if AE would also be included in the perimeter of ABCDEF?

Thanks,
Sri

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Uva@90: Master | Next Rank: 500 Posts; Posts: 490; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » Sat Nov 30, 2013 7:12 pm

gmattesttaker2 wrote:Hello,

Can you please assist with this:

In the figure above, polygon ABCDEF is equilateral and has perimeter 42. If AB is
parallel to ED, AF is parallel to BC, EF is parallel to CD, and x equals 60
degrees, what is the length of line segment BD (not shown)?

OA: [spoiler]7.sqroot(3)[/spoiler]

Hi Sri,
Given: X = 60 Degree and each side of length 7
We need to find Length of BD.
Length of BD = Length of AE.

Draw a line Joining B and E and it Intersects Line FC, lets keep that point as G.
Now AE = AG+GE

Consider triangle AFG.
It forms a 30:60:90 Triangle.
Whose sides will be in the ration x:âˆš3X:2X
we know that side for the angle 90 is 7
hence 2X = 7 => X = 7/2
we need AG which is formed by 60 degree angle,
So AG = (7/2)*âˆš3

Similarly do for another triangle, FGE
you will end up GE = (7/2)*âˆš3

Hence AE = (7/2)*âˆš3+ (7/2)*âˆš3 = 7âˆš3

BD = 7âˆš3

Hope it helps you.

Regards,
Uva.

Known is a drop Unknown is an Ocean

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Sat Nov 30, 2013 11:01 pm

gmattesttaker2 wrote:Hello,

Can you please assist with this:

In the figure above, polygon ABCDEF is equilateral and has perimeter 42. If AB is
parallel to ED, AF is parallel to BC, EF is parallel to CD, and x equals 60
degrees, what is the length of line segment BD (not shown)?

OA: [spoiler]7.sqroot(3)[/spoiler]

Join BD, drop CQ perpendicular on BD, this would create two identical 30-60-90 triangles in which BQ = QD = 3.5âˆš3 by property; hence BD = 7âˆš3.

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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