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How many non-congruent triangles with perimeter 7 have integer side le

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How many non-congruent triangles with perimeter 7 have integer side le  [#permalink]

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New post 19 Mar 2019, 02:09
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

56% (01:27) correct 44% (01:49) wrong based on 18 sessions

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Re: How many non-congruent triangles with perimeter 7 have integer side le  [#permalink]

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New post 19 Mar 2019, 06:12
Bunuel wrote:
How many non-congruent triangles with perimeter 7 have integer side lengths?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5


sum of three sides of triangle <7 ;
only possible when we have sides 1,3,2 or 2,2,1 since for triangle sum of two sides has to be >3rd side
IMO B
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Re: How many non-congruent triangles with perimeter 7 have integer side le  [#permalink]

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New post 23 Mar 2019, 14:06
Archit3110 wrote:
Bunuel wrote:
How many non-congruent triangles with perimeter 7 have integer side lengths?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5


sum of three sides of triangle <7 ;
only possible when we have sides 1,3,2 or 2,2,1 since for triangle sum of two sides has to be >3rd side
IMO B



The perimeter of the triangles should be 7, right?
For 1,3,2 - Perimeter = 6
For 2,2,1 - Perimeter = 5
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Re: How many non-congruent triangles with perimeter 7 have integer side le  [#permalink]

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New post 23 Mar 2019, 14:35
Cases where perimeter = 7

1) 1-2-4 ; Dropped since 1 + 2 < 4
2) 2-2-3 ; Valid case
3) 1-1-5 ; Dropped since 1 + 1 < 5

What case did I miss?
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Re: How many non-congruent triangles with perimeter 7 have integer side le  [#permalink]

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New post 23 Mar 2019, 19:27
yashjain800 wrote:
Cases where perimeter = 7

1) 1-2-4 ; Dropped since 1 + 2 < 4
2) 2-2-3 ; Valid case
3) 1-1-5 ; Dropped since 1 + 1 < 5

What case did I miss?


You missed the case (1,3,3)..

2-2-3 is a valid case
1-3-3 is a valid case.

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Re: How many non-congruent triangles with perimeter 7 have integer side le   [#permalink] 23 Mar 2019, 19:27
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