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Two sides of a triangle have length 6 and 8. Which of the fo

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Senior Manager
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Joined: 20 May 2014
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Kudos [?]: 49 [0], given: 220

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Two sides of a triangle have length 6 and 8. Which of the fo [#permalink] New post 26 Oct 2017, 02:29
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100% (00:37) correct 0% (00:00) wrong based on 1 sessions
Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle?

I. 2
II. 12
III. 24

A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II, and III


Kudos for correct solution.
[Reveal] Spoiler: OA
Director
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Joined: 03 Sep 2017
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Kudos [?]: 327 [0], given: 66

Re: Two sides of a triangle have length 6 and 8. Which of the fo [#permalink] New post 26 Oct 2017, 04:37
Given two sides of a triangle, the smallest area is almost zero when the two sides are almost coincident, while the largest area is the one when the two sides are perpendicular, thus the one of the right triangle of legs 6 and 8.

Thus, the range of possible areas goes from \(0^+\leq Area\leq \frac{6*8}{2}=24\). Thus, all the three areas are possible and answer is E
Re: Two sides of a triangle have length 6 and 8. Which of the fo   [#permalink] 26 Oct 2017, 04:37
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Two sides of a triangle have length 6 and 8. Which of the fo

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