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What is the greatest possible area of a triangular region wi
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25 Jul 2020, 09:45
25 Jul 2020, 09:45
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92% (01:22) correct
8% (02:10) wrong based on 25 sessions
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What is the greatest possible area of a triangular region with one side that corresponds with the diameter of a circle with radius 6, and the other vertex of the triangle on the circle?
(A) 24
(B) 36
(C) 40
(D) 48
(E) 72
(A) 24
(B) 36
(C) 40
(D) 48
(E) 72
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Joined: 25 Jul 2020
Posts: 38
Given Kudos: 0
GRE 1: Q170 V157
Re: What is the greatest possible area of a triangular region wi
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25 Jul 2020, 11:06
25 Jul 2020, 11:06
1
See the attached image. The key is to place the vertex in such a way that dropping a perpendicular from it will go through the center of the circle. Area is base * height = 36.
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gre123.png [ 7.43 KiB | Viewed 2031 times ]
Re: What is the greatest possible area of a triangular region wi
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26 Jul 2020, 09:13
26 Jul 2020, 09:13
2
Since the base will be same for all such triangles but height will vary, the triangle with maximum area will be the one where the perpendicular dropped from the third vertex on the side coinciding with the diameter passes through the center (the yellow triangle present in the figure).
So,
Max area = (1/2)*(12)*(6) = 36
Answer is B.
So,
Max area = (1/2)*(12)*(6) = 36
Answer is B.
Attachments
answer.png [ 11.49 KiB | Viewed 2016 times ]
