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

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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, 03:52
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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
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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, 07:33
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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Re: Which of the following is a possible length for side AB of triangle AB  [#permalink]

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New post 08 Sep 2018, 08:24
guys - the mistake a lot of ppl are making is to assume II. is 9+(3^0.5) which is not what it states.

The correct way to read this is II. is 9*(3^0.5). Which, when solved, does not satisfy the almighty triangle rules.
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Re: Which of the following is a possible length for side AB of triangle AB   [#permalink] 08 Sep 2018, 08:24

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