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# If ABC is an equilateral triangle, and BC=4

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If ABC is an equilateral triangle, and BC=4 [#permalink]  03 Sep 2019, 06:34
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Question Stats:

58% (02:22) correct 41% (02:55) wrong based on 12 sessions
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If ABCABC is an equilateral triangle,.png [ 4.97 KiB | Viewed 927 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

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Brent Hanneson – Creator of greenlighttestprep.com
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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: 2608
Followers: 95

Kudos [?]: 2812 [1] , given: 45

Re: If ABC is an equilateral triangle, and BC=4 [#permalink]  03 Sep 2019, 06:37
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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
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Brent Hanneson – Creator of greenlighttestprep.com
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Intern
Joined: 03 Nov 2019
Posts: 11
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Kudos [?]: 9 [2] , given: 3

Re: If ABC is an equilateral triangle, and BC=4 [#permalink]  02 Dec 2019, 14:17
2
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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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# If ABC is an equilateral triangle, and BC=4

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