arthuro69 wrote:
What is the perimeter of an equilateral triangle inscribed in a circle of radius 4 ?
A. \(6\sqrt{2}\)
B. \(6\sqrt{3}\)
C. \(12\sqrt{2}\)
D. \(12\sqrt{3}\)
E. \(24\)
So, here's what the diagram looks like.
If we draw lines from the center to each vertex, we get the following:
Since the radii have length 4, we can add that here:
Now we'll draw a line from the center that is PERPENDICULAR to one side of the tirangle.
We now have a SPECIAL 30-60-90 right triangle.
Here's the base version of this SPECIAL TRIANGLE
We can see that the each 30-60-90 triangle in the diagram is TWICE as big as the base version. So, each side opposite the 60º angle must have length 2√3
This means ONE side of the equilateral triangle has length 4√3, so the PERIMETER = 4√3 + 4√3 + 4√3 = 12√3
Answer: C
Cheers,
Brent
_________________
Brent Hanneson – Creator of gmatprepnow.com
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
Many students fail to maximize their quant score NOT because they lack the skills to solve certain questions but because they don’t understand what the GMAT is truly testing -
Learn more