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Two sides of a triangle measure 4 and 12. Which one of the following c

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Two sides of a triangle measure 4 and 12. Which one of the following c  [#permalink]

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New post 05 Apr 2019, 01:33
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A
B
C
D
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Question Stats:

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Two sides of a triangle measure 4 and 12. Which one of the following could equal the length of the third side?

(A) 5
(B) 7
(C) 9
(D) 17
(E) 20
Spoiler: OA

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Re: Two sides of a triangle measure 4 and 12. Which one of the following c  [#permalink]

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New post 05 Apr 2019, 01:46
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In any given triangle with sides A, B and C the sum of the lengths of any two sides of a triangle must be greater than the third side:

12-4<side<12+4
8<side<16
Only C : 9 satisfies the condition.
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Re: Two sides of a triangle measure 4 and 12. Which one of the following c  [#permalink]

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New post 05 Apr 2019, 02:08
Triangle property states that sum of two sides should be greater than third side and difference of two sides should be less than third side
Values of Side1 = 4, Side2 = 12 so

Side3 < Side2 + Side1 and Side3 > Side2 - Side1

12-4 < Side3 < 12+4
from options only value C satisfies

Answer is C
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Re: Two sides of a triangle measure 4 and 12. Which one of the following c  [#permalink]

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New post 05 Apr 2019, 03:39
Bunuel wrote:
Two sides of a triangle measure 4 and 12. Which one of the following could equal the length of the third side?

(A) 5
(B) 7
(C) 9
(D) 17
(E) 20


The property for a triangle to exist

Sum of any two sides of triangle > Third side of the triangle

i.e. if the third side = x then

4+x > 12 and 4+12 > x
i.e. x > 8 and x < 16

9 is the only acceptable value of x out of the given options hence

Answer: Option C
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Re: Two sides of a triangle measure 4 and 12. Which one of the following c  [#permalink]

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New post 05 Apr 2019, 03:43
Bunuel wrote:
Two sides of a triangle measure 4 and 12. Which one of the following could equal the length of the third side?

(A) 5
(B) 7
(C) 9
(D) 17
(E) 20


third side can be < 4+12 ; 16
and >12-4 ; 8
only 9 matches
IMO C
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Re: Two sides of a triangle measure 4 and 12. Which one of the following c   [#permalink] 05 Apr 2019, 03:43
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