Brent@GMATPrepNow wrote:
If ABC is an equilateral triangle, and BC=4√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

Answer: C
Source: www.gmatprepnow.com
Difficulty level: 650-700

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√3, and since BX = n, we know that side XC=4√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.

Answer: C

Cheers,
Brent