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

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Bunuel
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A certain triangle has a perimeter of 24. Which of the following could [#permalink] New post   16 Jun 2019, 23:50
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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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A
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Re: A certain triangle has a perimeter of 24. Which of the following could [#permalink] New post   17 Jun 2019, 00:02
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In any given triagle, the lengths of any two sides of the triangle must add up to more than the length of the third side.

II. If one of the sides is 12, the sum of lengths of the other two sides must be 12

III. If one of the sides is 14, the sum of lengths of the other two sides must be 10

Therefore II and III are not possible

Answer is (A)

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Re: A certain triangle has a perimeter of 24. Which of the following could [#permalink] New post   17 Jun 2019, 08:34
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Bunuel wrote:
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


third side rule of ∆ ; sum of two sides of ∆ > third side
here total sum = 14 so if 1 given side is 10 then other side total>10 is possible to match perimeter
where as 12 & 14 are > half of perimeter and will not be > sum of other two sides
IMO A
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Re: A certain triangle has a perimeter of 24. Which of the following could [#permalink] New post   02 Jul 2019, 10:37
Bunuel wrote:
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


Perimeter of a Triangle => 2(L+B) = 24
Or, L+B = 12

Among the answer choices, Only 10 works ! ( 10 + 2 )

QA: A
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Re: A certain triangle has a perimeter of 24. Which of the following could [#permalink] New post   08 Feb 2023, 14:01
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Bunuel wrote:
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



We can use the triangle inequality theorem in which the sum of any two sides must be greater than the third.

If one side is 10, the sum of the other two sides is 14. Thus, 10 works.

If one side is 12, the sum of the other two sides is 12. Thus, 12 does not work.

If one side is 14, the sum of the other two sides is 10. Thus, 14 does not work.

Answer: A
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Re: A certain triangle has a perimeter of 24. Which of the following could [#permalink]
08 Feb 2023, 14:01
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