Carcass wrote:
In the figure shown, the length of line segment QS is \(4\sqrt{3}\). What is the perimeter of equilateral triangle PQR?
A. \(12\)
B. \(12 \sqrt{3}\)
C. \(24\)
D. \(24 \sqrt{3}\)
E. \(48\)
Let's first add the given information to the diagram.
If ∆PQR is an equilateral triangle, then the 3 angles are each 60°
At this point, we can see we have a special 30-60-90 right triangle, which we can compare with the
BASE 30-60-90 right triangle When we compare the sides that are opposite the 60° angle, we can see that
4√3 is 4 times the value of
√3So, the magnification factor is 4.
This means the other 2 lengths will be 4 times the sides of the BASE 30-60-90 right triangle
Now that we know that each side has length 8, the perimeter = 8 + 8 + 8 = 24
Answer: C
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep