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

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Bunuel
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In triangle ABC, side AB = 3 and side BC = 8. Which of the following [#permalink] New post   18 Jan 2019, 00:22
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A
B
C
D
E

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5% (low)

Question Stats:

84% (01:01) correct 16% (01:33) wrong based on 73 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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E
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Re: In triangle ABC, side AB = 3 and side BC = 8. Which of the following [#permalink] New post   18 Jan 2019, 07:00
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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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Re: In triangle ABC, side AB = 3 and side BC = 8. Which of the following [#permalink] New post   19 Jan 2019, 00:29
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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
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Re: In triangle ABC, side AB = 3 and side BC = 8. Which of the following [#permalink] New post   15 Oct 2020, 22:41
Quote:
In triangle ABC, side AB = 3 and side BC = 8. Which of the following CANNOT be the perimeter of triangle ABC?

Step 1: Understanding the question
When two sides of a triangle is given, then the third side lies between difference and sum of the two given sides
8-3 < Third side < 8+3
5 < Third side < 11

Possible range of perimeter is:
3+8+5 < Perimeter < 3+8+11
16 < Perimeter < 22

E is correct
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Re: In triangle ABC, side AB = 3 and side BC = 8. Which of the following [#permalink] New post   17 Oct 2020, 13:09
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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

Solution:

Recall that the length of the longest side of a triangle is less than the sum of the lengths of the two shorter sides. Therefore, if AC is the longest side of triangle ABC, then AC < 3 + 8 = 11, and the perimeter of triangle ABC must be less than 3 + 8 + 11 = 22. Since the perimeter is less than 22, it can’t be 22.

Answer: E
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Re: In triangle ABC, side AB = 3 and side BC = 8. Which of the following [#permalink]
17 Oct 2020, 13:09
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