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

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Math Expert
Joined: 02 Sep 2009
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Which of the following can be the ratio of sides of a triangle?  [#permalink]

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28 Feb 2016, 08:26
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67% (00:35) correct 33% (00:36) wrong based on 135 sessions

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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

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Concentration: Operations
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Re: Which of the following can be the ratio of sides of a triangle?  [#permalink]

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29 Feb 2016, 12:15
For any triangle with sides a,b,c, the following rules for sides MUST be followed:

|a-b| << c << a+b (this has to be true for ALL the sides!)

II and III: both satisfy the conditions
Hence, Ans: D
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Re: Which of the following can be the ratio of sides of a triangle?  [#permalink]

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29 Feb 2016, 21:35
1
Bunuel wrote:
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

The sum of any two sides of a triangle must be greater than the third side.

I. $$3:\sqrt{4}:5$$
The ratio of sides are 3, 2 and 5
But 3 + 2 = 5 which is not acceptable. The sum of any two sides must be greater than the third side.
Hence these cannot be the ratio of the sides of the triangle.

II. $$\sqrt{3}:4:5$$

The ratio of sides are 1.7, 4 and 5.
The sum of any two is greater than the third.
So these can be the ratio of the sides of the triangle.

III. $$3:4:\sqrt{5}$$

The ratio of sides are 3, 4 and 2.2
The sum of any two is greater than the third.
So these can be the ratio of the sides of the triangle.

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Karishma
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Save up to $1,000 on GMAT prep through 8/20! Learn more here > GMAT self-study has never been more personalized or more fun. Try ORION Free! Manager Joined: 11 Jun 2016 Posts: 75 Location: India GMAT 1: 680 Q49 V35 GMAT 2: 690 Q49 V34 GPA: 3.4 Re: Which of the following can be the ratio of sides of a triangle? [#permalink] ### Show Tags 05 Dec 2017, 00:32 VeritasPrepKarishma wrote: Bunuel wrote: 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 The sum of any two sides of a triangle must be greater than the third side. I. $$3:\sqrt{4}:5$$ The ratio of sides are 3, 2 and 5 But 3 + 2 = 5 which is not acceptable. The sum of any two sides must be greater than the third side. Hence these cannot be the ratio of the sides of the triangle. II. $$\sqrt{3}:4:5$$ The ratio of sides are 1.7, 4 and 5. The sum of any two is greater than the third. So these can be the ratio of the sides of the triangle. III. $$3:4:\sqrt{5}$$ The ratio of sides are 3, 4 and 2.2 The sum of any two is greater than the third. So these can be the ratio of the sides of the triangle. Answer (D) VeritasPrepKarishma, Bunuel, Is it sufficient to just check for condition - The sum of any two is greater than the third. or do we also have to check that the difference of any two sides should be less than the third side Thanks Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8184 Location: Pune, India Re: Which of the following can be the ratio of sides of a triangle? [#permalink] ### Show Tags 05 Dec 2017, 01:34 KGump wrote: VeritasPrepKarishma wrote: Bunuel wrote: 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 The sum of any two sides of a triangle must be greater than the third side. I. $$3:\sqrt{4}:5$$ The ratio of sides are 3, 2 and 5 But 3 + 2 = 5 which is not acceptable. The sum of any two sides must be greater than the third side. Hence these cannot be the ratio of the sides of the triangle. II. $$\sqrt{3}:4:5$$ The ratio of sides are 1.7, 4 and 5. The sum of any two is greater than the third. So these can be the ratio of the sides of the triangle. III. $$3:4:\sqrt{5}$$ The ratio of sides are 3, 4 and 2.2 The sum of any two is greater than the third. So these can be the ratio of the sides of the triangle. Answer (D) VeritasPrepKarishma, Bunuel, Is it sufficient to just check for condition - The sum of any two is greater than the third. or do we also have to check that the difference of any two sides should be less than the third side Thanks These are just different ways of saying the same thing. a + b > c or a > c - b Say sides are 2, 3 and 6. Sum of 2 and 3 is not greater than 6. Also difference of 6 and 3 is not less than 2. _________________ Karishma Veritas Prep GMAT Instructor Save up to$1,000 on GMAT prep through 8/20! Learn more here >

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Re: Which of the following can be the ratio of sides of a triangle?  [#permalink]

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05 Dec 2017, 01:42
VeritasPrepKarishma wrote:

These are just different ways of saying the same thing.

a + b > c
or
a > c - b

Say sides are 2, 3 and 6.
Sum of 2 and 3 is not greater than 6.
Also difference of 6 and 3 is not less than 2.

Oh.. i see now.. always had this stupid doubt..
Thankyou for clearing this
Re: Which of the following can be the ratio of sides of a triangle? &nbs [#permalink] 05 Dec 2017, 01:42
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