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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
Posts: 53066
Which of the following can be the ratio of sides of a triangle?  [#permalink]

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28 Feb 2016, 07:26
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Difficulty:

25% (medium)

Question Stats:

71% (01:10) correct 29% (01:18) wrong based on 192 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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Joined: 23 Jan 2015
Posts: 38
Location: India
Concentration: Operations
WE: Information Technology (Computer Software)
Re: Which of the following can be the ratio of sides of a triangle?  [#permalink]

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29 Feb 2016, 11:15
1
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, 20:35
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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Re: Which of the following can be the ratio of sides of a triangle?  [#permalink]

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04 Dec 2017, 23:32
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.

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
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Joined: 16 Oct 2010
Posts: 8891
Location: Pune, India
Re: Which of the following can be the ratio of sides of a triangle?  [#permalink]

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05 Dec 2017, 00:34
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.

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.
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Karishma
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Joined: 11 Jun 2016
Posts: 73
Location: India
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GMAT 2: 690 Q49 V34
GPA: 3.4
Re: Which of the following can be the ratio of sides of a triangle?  [#permalink]

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05 Dec 2017, 00:42
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
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Re: Which of the following can be the ratio of sides of a triangle?  [#permalink]

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12 Jan 2019, 21:31
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Re: Which of the following can be the ratio of sides of a triangle?   [#permalink] 12 Jan 2019, 21:31
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