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

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Director
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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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New post 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

The correct answer is (C)

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

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

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

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New post 03 Jun 2017, 04:38
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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.

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

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New post 04 Jun 2017, 02:52
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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
Answer C

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

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

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New post 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.

Answer: C
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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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