The above shape is made of eight identical equilateral triangles, each

Question

https://gmatclub.com/forum/download/file.php?id=58786 The above shape is made of eight identical equilateral triangles, each having a perimeter of 3. What is the straight-line distance between points P and Q? A. √3 B. 3 C. 4 D. 2√2 E. 2√3 1.png

Sumi1010 · Answer

AS the perimeter is 3 units, the side of each equilateral triangle is 1 unit.

Thus, the straight line distance between  P  to  mid-pt of P and Q  =
sq root (2^2 - 1^2) = sq root (3).
 Thus distance between P and Q = 
2 x sq root (3)

E

CrackverbalGMAT · Answer

Another method is to use the height of the equilateral triangle =  \frac{\sqrt{3}}{2} a, where a is the side of the triangle.

The perimeter of the equilateral triangle is given as 3, therefore each side = 1.

The height is =  \frac{\sqrt{3}}{2}

The straight line distance = 4 * height = 4 *  \frac{\sqrt{3}}{2}  = 2 \sqrt{3}

Option E

Arun Kumar

dortinator1234923 · Answer

Each side is 1 (P=3, so 1+1+1)

Length from P to the Mid = 2 and From bottom to the Mid = 1

Apply Pythagoras->
a^2 + b2 = c2

In this case: c^2 - b^2 = a^2
√(length^2 - bottom to mid^2) = √(P to Mid)
√(2^2 - 1^2) = √(3).

This is the point from P to the Mid , but we need from P to Q

2 * (P to M) = PQ
2 * √(3) = 2√(3)

Answer is E

ScottTargetTestPrep · Answer

Solution:
 
We see that the straight-line distance between points P and Q is 4 times the height of one equilateral triangle. Since an equilateral triangle has a perimeter of 3, it has side length of 1 and a height of 1/2 x 1 x √3 = √3/2 (recall that the height of an equilateral triangle is half of its side length times √3). Therefore, PQ = 4 x √3/2 = 2√3.

Answer: E

The above shape is made of eight identical equilateral triangles, each

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

The above shape is made of eight identical equilateral triangles, each

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards