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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # If ABC is an equilateral triangle, and BC=4  Question banks Downloads My Bookmarks Reviews Important topics
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TAGS: GRE Instructor Joined: 10 Apr 2015
Posts: 3290
Followers: 127

Kudos [?]: 3700  , given: 62

If ABC is an equilateral triangle, and BC=4 [#permalink]
1
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Expert's post 00:00

Question Stats: 61% (02:35) correct 38% (02:55) wrong based on 13 sessions
Attachment: If ABCABC is an equilateral triangle,.png [ 4.97 KiB | Viewed 1473 times ]

If $$ABC$$ is an equilateral triangle, and $$BC=4\sqrt{3}$$, what is the approximate length
of one side of square $$WXYZ$$?

A) 1.9
B) 2.9
C) 3.2
D) 4.1
E) 4.6
[Reveal] Spoiler: OA

_________________

Brent Hanneson – Creator of greenlighttestprep.com Last edited by Carcass on 27 Nov 2019, 11:28, edited 2 times in total.
Edited by Carcass GRE Instructor Joined: 10 Apr 2015
Posts: 3290
Followers: 127

Kudos [?]: 3700  , given: 62

Re: If ABC is an equilateral triangle, and BC=4 [#permalink]
1
KUDOS
Expert's post
GreenlightTestPrep wrote:
Attachment:
Z04.png

If $$ABC$$ is an equilateral triangle, and $$BC=4\sqrt{3}$$, what is the approximate length
of one side of square $$WXYZ$$?

A) 1.9
B) 2.9
C) 3.2
D) 4.1
E) 4.6

Since $$ABC$$ is an equilateral triangle, we know the following angles are 60° each.
Also, let's let n = the length of each side of the square Since BWX is also an equilateral triangle, we know that all 3 sides have length n: Since $$BC=4\sqrt{3}$$, and since $$BX = n$$, we know that side $$XC=4\sqrt{3}-n$$ At this point, we can see that triangle XYC is a special 30-60-90 right triangle. When we compare ∆XYC with the base 30-60-90 triangle, we can compare corresponding sides to create the following equation: (4√3 - n)/2 = n/√3
Cross multiply to get: (√3)(4√3 - n)= (2)(n)
Simplify to get: 12 - (√3)n = 2n
Add (√3)n to both sides to get: 12 = 2n + (√3)n
Factor right side to get: 12 = n(2 + √3)
Divide both sides by (2 + √3) to get: n = 12/(2 + √3)

PRO TIP #1: By test day, all students should have the following approximations memorized:
√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2
So, 12/(2 + √3) ≈ 12/(2 + 1.7) ≈ 12/3.7

PRO TIP #2: We need not calculate the actual value of 12/3.7
Instead, notice that 12/3 = 4 and 12/4 = 3
Since 3.7 is BETWEEN 3 and 4, we now that 12/3.7 must be between 3 and 4
In other words, 12/3.7 = 3.something.

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com  Intern Joined: 03 Nov 2019
Posts: 11
Followers: 0

Kudos [?]: 12  , given: 3

Re: If ABC is an equilateral triangle, and BC=4 [#permalink]
2
KUDOS
Could anyone give feedback on my approach?
So my logic was that the corner X of the square was fairly in the middle of segment BC.
Then,
4(sqrt(3)) is approximately 6.9
6.9/2 is 3.45

The closest option we have is 3.2 (option C). Re: If ABC is an equilateral triangle, and BC=4   [#permalink] 02 Dec 2019, 14:17
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