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# If 13/4, 21/4 and k are sides of a triangle and k is an integer, what

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If 13/4, 21/4 and k are sides of a triangle and k is an integer, what  [#permalink]

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11 Sep 2018, 02:02
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If 13/4, 21/4 and k are sides of a triangle and k is an integer, what is the smallest possible value of k?

A. 1
B. 2
C. 3
D. 4
E. 5

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Re: If 13/4, 21/4 and k are sides of a triangle and k is an integer, what  [#permalink]

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11 Sep 2018, 02:06
The third side of a triangle should be greater than the difference between the other two sides and less than the sum of the other two sides.

21/4-13/4 < K < 21/4+13/4

2 < K < 8.5

Smallest possible value is 3.

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Re: If 13/4, 21/4 and k are sides of a triangle and k is an integer, what  [#permalink]

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11 Sep 2018, 06:48
Bunuel wrote:
If 13/4, 21/4 and k are sides of a triangle and k is an integer, what is the smallest possible value of k?

A. 1
B. 2
C. 3
D. 4
E. 5

The least value of the third side should be atleast greater than the difference of the other two sides.
therefore,
$$(\frac{21}{4}-\frac{13}{4})<K$$
$$8/4<K$$
$$2<K$$

therefore least value of K is 3

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Re: If 13/4, 21/4 and k are sides of a triangle and k is an integer, what  [#permalink]

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12 Sep 2018, 18:32
Bunuel wrote:
If 13/4, 21/4 and k are sides of a triangle and k is an integer, what is the smallest possible value of k?

A. 1
B. 2
C. 3
D. 4
E. 5

13/4 = 3.25

21/4 = 5.25

Since the sum of any two sides of a triangle must be greater than the third, the smallest possible integer value of k is 3 so that 3.25 + 3 > 5.25.

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Re: If 13/4, 21/4 and k are sides of a triangle and k is an integer, what   [#permalink] 12 Sep 2018, 18:32
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