Which of the following can be the ratio of sides of a triangle?

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

Which of the following can be the ratio of sides of a triangle?

by BTGmoderatorDC » Mon Jan 13, 2020 6:27 pm

Which of the following can be the ratio of sides of a triangle?

I. \(3:\sqrt{4}:5\)
II. \(\sqrt{3}:4:5\)
III. \(3:4:\sqrt{5}\)

A. II only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III

OA D

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Mon Jan 13, 2020 6:27 pm

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8085; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: Which of the following can be the ratio of sides of a triangle?

by Scott@TargetTestPrep » Thu Jan 16, 2020 6:46 am

BTGmoderatorDC wrote: ↑
Mon Jan 13, 2020 6:27 pm
Which of the following can be the ratio of sides of a triangle?

I. \(3:\sqrt{4}:5\)
II. \(\sqrt{3}:4:5\)
III. \(3:4:\sqrt{5}\)

A. II only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III

OA D

In order to be the ratio of the sides of a triangle, the sum of the two smaller numbers should be greater than the largest number.

In I, the largest number is 5, but 3 + √4 = 3 + 2 = 5, which is not greater than 5. So I can’t be the ratio of the sides of a triangle.

In II, the largest number is also 5, and √3 + 4 ≈ 1.7 + 4 = 5.7, which is greater than 5. So II can be the ratio of the sides of a triangle.

In III, the largest number is 4, and 3 + √5 ≈ 3 + 2.2 = 5.2, which is greater than 4. So III can be the ratio of the sides of a triangle.

Answer: D