In the figure above, PQR and STU are identical equilateral triangles…
We are given a diagram with triangles PQR and STU. We are also given that PQR and STU are identical equilateral triangles, and PQ = 6. Finally, we are asked to determine the perimeter of polygon PQWTUVR. Since side PQ = 6, we know that the perimeter of each triangle is 18. However, to determine the perimeter of polygon PQWTUVR, we must subtract the perimeter of triangle SWV from the combined perimeters of the two larger triangles. We have presented this idea in the diagram below.
Statement One Alone:
Triangle SWV has perimeter 9.
Since we are given the perimeter of triangle SWV, we can determine the perimeter of polygon PQWTUVR.
PQWTUVR = 36 – 9 = 27
Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C and E.
Statement Two Alone:
VW has length 3.5.
Only knowing the length of VW is not enough to determine the perimeter of polygon PQWTUVR.