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# Which of the following is a possible length for side AB of triangle AB

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Director
Joined: 12 Nov 2016
Posts: 791

Kudos [?]: 39 [0], given: 166

Re: Which of the following is a possible length for side AB of triangle AB [#permalink]

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19 Apr 2017, 21:32
jimmyjamesdonkey wrote:
Which of the following is a possible length for side AB of triangle ABC if AC = 6 and BC = 9?

I. 3
II. 9 √3
III. 13.5

(A) I only
(B) II only
(C) III only
(D) II and III
(E) I, II, and III

We can approach this problem with triangle properties in mind; though, first it is important to note that the stem does not state that this triangle is a right triangle so the Pythagorean Theorem cannot be applied:

(I) The sums of the two smaller sides of a triangle must be larger than the hypotenuse or greatest side- "3" fails this test and is therefore not a viable option
(II) If considered 9 √3 as 9(1.7) = 15.3 which is larger than 6 + 9 and thus not a viable option
(III) 13.5 is smaller than the sum of 9 and 6 and therefore a viable option

Kudos [?]: 39 [0], given: 166

Intern
Joined: 24 May 2016
Posts: 19

Kudos [?]: 9 [1], given: 163

Location: Germany
Which of the following is a possible length for side AB of triangle AB [#permalink]

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03 Jun 2017, 04:38
1
KUDOS
As pointed out earlier, the question is based on the triangle inequality theorem:
In that case AB has to be smaller than the sum of the two given sides 9+6=15 and be bigger than their difference 9-6=3
Thus you can write the inequality as follows: 3<AB<15.
If you now test the options only Roman Numeral III fits in that range, so the answer is C.

Kudos [?]: 9 [1], given: 163

Manager
Joined: 19 Aug 2015
Posts: 120

Kudos [?]: 5 [1], given: 24

Location: India
GMAT 1: 650 Q49 V30
Which of the following is a possible length for side AB of triangle AB [#permalink]

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04 Jun 2017, 02:52
1
KUDOS
jimmyjamesdonkey wrote:
Which of the following is a possible length for side AB of triangle ABC if AC = 6 and BC = 9?

I. 3
II. 9 √3
III. 13.5

(A) I only
(B) II only
(C) III only
(D) II and III
(E) I, II, and III

Sum of two sides should be greater than third side
if AB =3? then $$AB+AC=BC$$so wrong
if $$AB=9\sqrt{3}$$ then $$AC+BC<AB$$so wrong
if AB=13.5 then $$AC+BC>AB$$ so correct

Kudos [?]: 5 [1], given: 24

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1820

Kudos [?]: 1048 [0], given: 5

Re: Which of the following is a possible length for side AB of triangle AB [#permalink]

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11 Dec 2017, 06:33
jimmyjamesdonkey wrote:
Which of the following is a possible length for side AB of triangle ABC if AC = 6 and BC = 9?

I. 3
II. 9 √3
III. 13.5

(A) I only
(B) II only
(C) III only
(D) II and III
(E) I, II, and III

This problem is testing us on the triangle inequality theorem in which the sum of the lengths any two sides of a triangle MUST be greater than that of the third side. Let’s test each Roman numeral to determine which could be a possible side length of AB. Keep in mind that AC = 6 and BC = 9.

I. 3

Since 6 + 3 IS NOT greater than 9, 3 cannot be the length of side AB.

II. 9√3

9√3 is roughly equal to 9 x 1.7 = 15.3, and since 6 + 9 IS NOT greater than 15.3, 9√3 cannot be the length of side AB.

III. 13.5

Since 6 + 13.5 IS greater than 9, 13.5 + 9 IS greater than 6, and 9 + 6 IS greater than 13.5; thus, 13.5 could be the length of side AB.

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Jeffery Miller

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Kudos [?]: 1048 [0], given: 5

Re: Which of the following is a possible length for side AB of triangle AB   [#permalink] 11 Dec 2017, 06:33

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