siddhans wrote:

Attachment:

Triangle.png

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

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