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

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Math Expert
Joined: 02 Sep 2009
Posts: 59728
How many non-congruent triangles with perimeter 7 have integer side le  [#permalink]

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19 Mar 2019, 02:09
00:00

Difficulty:

35% (medium)

Question Stats:

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

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

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

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Posts: 5484
Location: India
Concentration: Sustainability, Marketing
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Re: How many non-congruent triangles with perimeter 7 have integer side le  [#permalink]

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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
Intern
Joined: 23 Mar 2018
Posts: 19
Re: How many non-congruent triangles with perimeter 7 have integer side le  [#permalink]

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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
Intern
Joined: 13 Jul 2018
Posts: 4
Re: How many non-congruent triangles with perimeter 7 have integer side le  [#permalink]

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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?
Manager
Joined: 19 Jan 2019
Posts: 110
Re: How many non-congruent triangles with perimeter 7 have integer side le  [#permalink]

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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.

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