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

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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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Question Stats:

72% (01:13) correct 28% (01:23) wrong based on 143 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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Re: Which of the following can be the ratio of sides of a triangle?  [#permalink]

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29 Feb 2016, 12:15
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, 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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Re: Which of the following can be the ratio of sides of a triangle?  [#permalink]

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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.

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

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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.

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

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18 Aug 2019, 17:08
Official Explanation:

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

4–√=2
. If the ratio of the sides is 3:2:5, the triangle cannot be formed because 3+2 is equal to 5, not greater.
3–√≈1.73
(however, all we need to know is that 3–√
is larger than 1 and smaller than 2). If the ratio of the sides is 1.73:4:5, the sum of any two sides will be greater than the third side. So the triangle can be formed.
5–√≈2.2
(again, we just need to know it is larger than 2 but smaller than 3). If the ratio of the sides is 3:4:2.2, the sum of any two sides will be greater than the third side. So the triangle can be formed.
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Re: Which of the following can be the ratio of sides of a triangle?   [#permalink] 18 Aug 2019, 17:08
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