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# In triangle ABC, side AB = 3 and side BC = 8. Which of the following

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Math Expert
Joined: 02 Sep 2009
Posts: 52905
In triangle ABC, side AB = 3 and side BC = 8. Which of the following  [#permalink]

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17 Jan 2019, 23:22
00:00

Difficulty:

15% (low)

Question Stats:

75% (01:03) correct 25% (01:30) wrong based on 24 sessions

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In triangle ABC, side AB = 3 and side BC = 8. Which of the following CANNOT be the perimeter of triangle ABC?

A 18
B 19
C 20
D 21
E 22

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Re: In triangle ABC, side AB = 3 and side BC = 8. Which of the following  [#permalink]

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18 Jan 2019, 06:00
Bunuel wrote:
In triangle ABC, side AB = 3 and side BC = 8. Which of the following CANNOT be the perimeter of triangle ABC?

A 18
B 19
C 20
D 21
E 22

third side < 8+3 ; <11
so it can be 10
so perimter max; 8 +3+10= 21

imo E is not valid
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Joined: 15 Feb 2018
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Re: In triangle ABC, side AB = 3 and side BC = 8. Which of the following  [#permalink]

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18 Jan 2019, 23:29
This question tests the Triangle Inequality Theorem.
The third length of a triangle cannot be equal to or shorter than the difference of the other two sides nor can it be larger than or equal to the sum of the other two sides

BC-AB<AC<BC+AB
8-3<AC<8+3
5<AC<11

Subtract 11 from each of the options. The only one that is not within the range is E as it adds 11 (CANNOT be equal to the sum)

E
Re: In triangle ABC, side AB = 3 and side BC = 8. Which of the following   [#permalink] 18 Jan 2019, 23:29
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