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

squareSince 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/

√3Cross 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/

3.7Instead, 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.

Answer: C

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

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