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# Triangle ABC has a perimeter of 18. Which of the following cannot be

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Math Expert
Joined: 02 Sep 2009
Posts: 55148
Triangle ABC has a perimeter of 18. Which of the following cannot be  [#permalink]

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20 Jul 2017, 21:38
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Difficulty:

55% (hard)

Question Stats:

50% (01:55) correct 50% (01:30) wrong based on 53 sessions

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Triangle ABC has a perimeter of 18. Which of the following cannot be the area of triangle ABC?

(A) 119/359
(B) 359/119
(C) π
(D) 12
(E) 16

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Triangle ABC has a perimeter of 18. Which of the following cannot be  [#permalink]

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21 Jul 2017, 00:49
Bunuel wrote:
Triangle ABC has a perimeter of 18. Which of the following cannot be the area of triangle ABC?

(A) 119/359
(B) 359/119
(C) π
(D) 12
(E) 16

It should be E. Even if the triangle is equilateral (side 6) in which case its area would be maximum, area cannot be 16.

$$A*\sqrt{3}/4$$

$$6*\sqrt{3}/4$$ $$= 15.59$$

Rest of the values are possible by playing with large and small values of base and height.
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Re: Triangle ABC has a perimeter of 18. Which of the following cannot be  [#permalink]

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28 Jul 2017, 08:19
1
2 rules to remember always in such questions
- For a given perimeter, equilateral triangle has the largest area
- For a given area, equilateral triangle has the smallest perimeter

With the above context, if perimeter is 18 then each side of an equilateral triangle will be 6

Area will be (sqrt)3*3*3/4=9(sqrt)3~15.3

Hence only option above 15 is E. Answer is E
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Re: Triangle ABC has a perimeter of 18. Which of the following cannot be   [#permalink] 28 Jul 2017, 08:19
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