The volume of the cube in the figure above is 64. If the vertices of ∆ PQR are midpoints of the cube's edges, what is the perimeter of ∆ PQR?

(A) 6
(B) 6√2
(C) 6√3
(D) 12
(E) 12√2


_________________

Find side length
\(s^3 = 64\)
\(\sqrt[3]{s^3} = \sqrt[3]{64}\)
\(s = 4\)


Perimeter?

Three two-dimensional triangles make up ∆ PQR (see diagram: ∆ PRS, ∆ QRS, and ∆ PQS)
Side length of all three = \(2\) (vertices at midpoint of cube's edges)
All three are congruent right isosceles triangles (45-45-90) with corresponding side ratios in length \(x : x : x\sqrt{2}\)

\(x = 2\), so hyptenuse of each two-dimensional triangle = \(2\sqrt{2}\)

Those hypotenuses are the perimeter of ∆ PQR. that is
Side length of ∆ PQR = \(2\sqrt{2}\)

Perimeter:
\(2\sqrt{2} + 2\sqrt{2} + 2\sqrt{2} = 6\sqrt{2}\)

Answer B
_________________

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________