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# A certain triangle has a perimeter of 24. Which of the following could

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A certain triangle has a perimeter of 24. Which of the following could  [#permalink]

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03 Sep 2017, 21:23
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25% (medium)

Question Stats:

75% (01:15) correct 25% (00:59) wrong based on 42 sessions

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A certain triangle has a perimeter of 24. Which of the following could be the length of one of the sides?
I. 10
II. 12
III. 14
A. I only
B. III only
C. I and II only
D. II and III only
E. I, II and III

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Re: A certain triangle has a perimeter of 24. Which of the following could  [#permalink]

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03 Sep 2017, 21:26
Sum of any two sides of a triangle is greater than third side.
If one side is
I - 10, sum of other two is 14 possible
II- 12, sum of other two is 12 not possible (as sum of any two sides should be greater than third side)
III-14, sum of other two is 10 not possible (as sum of any two sides should be greater than third side)
Thus I only, option A
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Re: A certain triangle has a perimeter of 24. Which of the following could  [#permalink]

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04 Sep 2017, 00:30
Given:
For a triangle a+b+c=24
Theory used: SUm of 2 sides of a triangle is always "greater" than 3rd side

1)a=10, so b+c=14
we can find different values of b and c to satisfy the condition.
Sufficient

2)a=12, so b+c=12,
Here sum of 2 sides becomes "equal to 3rd side". Not possible for a triangle.

3)a=14, so b+c=10,
Here sum of 2 sides becomes "less than 3rd side". Not possible for a triangle.

Re: A certain triangle has a perimeter of 24. Which of the following could   [#permalink] 04 Sep 2017, 00:30
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# A certain triangle has a perimeter of 24. Which of the following could

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