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04 Nov 2020, 02:00
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E
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Difficulty:
15%
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Question Stats:
82% (01:27) correct
18%
(01:45)
wrong
based on 50
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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
Attachment:
1.png [ 9.41 KiB | Viewed 1890 times ]
04 Nov 2020, 02:45
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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
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
04 Nov 2020, 05:54
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Bunuel
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
11 Nov 2020, 02:57
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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
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
