unceldolan wrote:

mau5 wrote:

emmak wrote:

A square with area 16 is perfectly inscribed inside an equilateral triangle. What is the perimeter of the triangle?

a) (83√3)3+4

b) 4√3+4

c) 8√3+12

d) 24+12

e) (32√3)3+12

As Bunuel has mentioned that GMAT doesn't test Trigonometry, I will give a geometric approach for this problem. Let's take the base of the triangle. The middle portion is of 4 units. The small right angle triangle formed to the left of the square has 4 units opposite 60 degrees. Thus, the side opposite 30 degrees is \(4/\sqrt{3}\). This will be same for the small right angle triangle on the right of the square too. Thus the total length of the base = 2*\(4/\sqrt{3}\)+4. Thus the perimeter of the triangle is \(3*(8/\sqrt{3} +4) = 8*\sqrt{3}+12.\)

C.

Hey mau5, could you explain how you knew that the opposite side of 30 degrees was \(4/\sqrt{3}\)? I follow your approach, but I don't get how you know that.Thanks!

A right angle triangle where the angles are 30:60:90 , the respective opposite sides are always in the ratio \(1:\sqrt{3}:2.\)

As the side opposite 60 degrees is 4, hence, the side opposite 30 degrees would be\(\frac{4}{\sqrt{3}}\)

For getting a thorough understanding, go through this :

math-triangles-87197.html
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