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yashikaaggarwal
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13 Jul 2020, 09:23
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
64% (02:25) correct
36%
(02:48)
wrong
based on 64
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In an Equilateral triangle, 3 coins of radii 1 unit each are kept in such a way that they touch each other and also the sides of the triangle. What is the area of triangle (in sq. units)?
A. 4+5√2
B. 6+4√3
C. 4+6√3
D. 3+8√3
E. 5+3√2
A. 4+5√2
B. 6+4√3
C. 4+6√3
D. 3+8√3
E. 5+3√2
yashikaaggarwal
Senior Moderator - Masters Forum
Joined: 19 Jan 2020
Last visit: 29 Mar 2026
Posts: 3,089
Given Kudos: 1,510
Location: India
Schools: Cranfield (A) Warwick MiM "23 (M)
GPA: 4
WE:Analyst (Internet and New Media)
15 Jul 2020, 09:27
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The radius of circle is one
The smaller triangle is a right angle triangle with 30, 60 and 90 degree as angle whose sides are x, √3*x, 2x
where x = 1 (on comparing)
therefore √3*x = √3
The Side of triangle = √3 + 2 + √3
=> 2√3 + 2
The area of equilateral triangle = √3/4*side^2
=> √3/4*(2√3 + 2)
=> 4√3 + 6 or 6 + 4√3
Answer is B
VERBAL1 you might be able to understand better with diagram. its pure methodological question.
The smaller triangle is a right angle triangle with 30, 60 and 90 degree as angle whose sides are x, √3*x, 2x
where x = 1 (on comparing)
therefore √3*x = √3
The Side of triangle = √3 + 2 + √3
=> 2√3 + 2
The area of equilateral triangle = √3/4*side^2
=> √3/4*(2√3 + 2)
=> 4√3 + 6 or 6 + 4√3
Answer is B
VERBAL1 you might be able to understand better with diagram. its pure methodological question.
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hsapril00B.gif [ 4.84 KiB | Viewed 3564 times ]
General Discussion
13 Jul 2020, 10:37
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In an equilateral triangle of side x, if 3 circles of equal radii are drawn touching each other, then the relation between the side and the radius is given as x = 2r (\(\sqrt{3}\) + 1)
Here r = 1, therefore the side of the equilateral triangle = 2 * 1 (\(\sqrt{3}\) + 1) = 2(\(\sqrt{3}\) + 1)
Area of an equilateral triangle = \(\frac{\sqrt{3}}{4}\) * \(x^{2}\)
Therefore Area = \(\frac{\sqrt{3}}{4}\) * [\(2(\sqrt{3} + 1)] ^2\)
Area = \(\frac{\sqrt{3}}{4}\) * 4 * (3 + 2*\(\sqrt{3}\) + 1)
A = \(\sqrt{3}\) * (4 + 2 * \(\sqrt{3}\))
A = 4\(\sqrt{3}\) + 6
Option B
Arun Kumar
Here r = 1, therefore the side of the equilateral triangle = 2 * 1 (\(\sqrt{3}\) + 1) = 2(\(\sqrt{3}\) + 1)
Area of an equilateral triangle = \(\frac{\sqrt{3}}{4}\) * \(x^{2}\)
Therefore Area = \(\frac{\sqrt{3}}{4}\) * [\(2(\sqrt{3} + 1)] ^2\)
Area = \(\frac{\sqrt{3}}{4}\) * 4 * (3 + 2*\(\sqrt{3}\) + 1)
A = \(\sqrt{3}\) * (4 + 2 * \(\sqrt{3}\))
A = 4\(\sqrt{3}\) + 6
Option B
Arun Kumar
