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In the figure shown, the length of line segment QS is
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11 Jun 2020, 02:09
11 Jun 2020, 02:09
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Question Stats:
82% (00:58) correct
17% (02:48) wrong based on 45 sessions
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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. \(48\)
Re: In the figure shown, the length of line segment QS is
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11 Jun 2020, 02:09
11 Jun 2020, 02:09
Expert Reply
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Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
Re: In the figure shown, the length of line segment QS is
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11 Jun 2020, 05:25
11 Jun 2020, 05:25
1
Since this is an equilateral triangle, we know that all sides are equal.
They give us the height of the equilateral triangle, which splits the equilateral triangle into 2 30-60-90 triangles.
Using the principles of a 30-60-90 triangle, we know that the sides will be in the ratio of x:x(sqrt)3:2x.
Plugging the side QS = 4(sqrt)3 into the ratio we get:
4: 4(sqrt)3 : 8
Now we know the hypotenuse of this isosceles triangle is equal to the side of the equilateral triangle (8). And, as an equilateral triangle, we know that all the sides are the same length. The perimeter is just adding up all 3 sides to get: 3(8) = 24. Answer is C.
They give us the height of the equilateral triangle, which splits the equilateral triangle into 2 30-60-90 triangles.
Using the principles of a 30-60-90 triangle, we know that the sides will be in the ratio of x:x(sqrt)3:2x.
Plugging the side QS = 4(sqrt)3 into the ratio we get:
4: 4(sqrt)3 : 8
Now we know the hypotenuse of this isosceles triangle is equal to the side of the equilateral triangle (8). And, as an equilateral triangle, we know that all the sides are the same length. The perimeter is just adding up all 3 sides to get: 3(8) = 24. Answer is C.
