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An equilateral triangle with perimeter p, a square and a semicircle w
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02 Jun 2021, 10:34
02 Jun 2021, 10:34
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Question Stats:
91% (02:07) correct
8% (01:08) wrong based on 12 sessions
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GRE An equilateral triangle with perimeter p.jpg [ 11.25 KiB | Viewed 1339 times ]
An equilateral triangle with perimeter p, a square, and a semicircle were joined to form the figure shown above. What is the perimeter of this figure?
A. \(3p\)
B. \(\frac{p}{2}+ \pi p\)
C. \(7p + \frac{\pi}{2} p\)
D. \(\frac{7}{3p} + \frac{\pi}{3} p\)
E. \(\frac{4}{3}p+\frac{\pi}{6}p\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: An equilateral triangle with perimeter p, a square and a semicircle w
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03 Jun 2021, 02:51
03 Jun 2021, 02:51
1
Carcass wrote:
Attachment:
GRE An equilateral triangle with perimeter p.jpg
An equilateral triangle with perimeter p, a square, and a semicircle were joined to form the figure shown above. What is the perimeter of this figure?
A. \(3p\)
B. \(\frac{p}{2}+ \pi p\)
C. \(7p + \frac{\pi}{2} p\)
D. \(\frac{7}{3p} + \frac{\pi}{3} p\)
E. \(\frac{4}{3}p+\frac{\pi}{6}p\)
Let the side of equilateral triangle be a
So, 3a = p
i.e. a = \(\frac{p}{3}\)
Also, side of equilateral triangle = side of square = diameter of semi-circle = \(\frac{p}{3}\)
Half-circumference of circle = \(πr = \frac{πp}{6}\)
Perimeter of other fours sides of the figure = \(4(\frac{p}{3})\)
Total Perimeter = \(\frac{4p}{3} + \frac{πp}{6}\)
Hence, option E
gmatclubot
Re: An equilateral triangle with perimeter p, a square and a semicircle w [#permalink]
03 Jun 2021, 02:51
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