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If 2/3, 38/8 and b are sides of a triangle and b is an integer, what i

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If 2/3, 38/8 and b are sides of a triangle and b is an integer, what i  [#permalink]

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New post 04 Sep 2018, 23:30
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

73% (01:36) correct 27% (01:48) wrong based on 22 sessions

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If 2/3, 38/8 and b are sides of a triangle and b is an integer, what i  [#permalink]

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New post 04 Sep 2018, 23:48
Bunuel wrote:
If 2/3, 38/8 and b are sides of a triangle and b is an integer, what is b?


A. 2
B. 3
C. 5
D. 6
E. 8


Concept: The sum of the smaller two sides of the triangle is greater than the largest side of the triangle

Given: Two of the sides of the triangle are \(\frac{2}{3} = 0.67\) and \(\frac{38}{8} = 4.75\) | The third side is b.

Therefore, as 0.67 + 4.75(2 smaller sides) > 5(the third side), the value of b is 5(Option C)

If b = 3(it is one of smaller sides). Here, \(3 + 0.67 < 4.75\) and this cannot be the value of b.
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If 2/3, 38/8 and b are sides of a triangle and b is an integer, what i  [#permalink]

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New post 07 Sep 2018, 14:27
Bunuel wrote:
If 2/3, 38/8 and b are sides of a triangle and b is an integer, what is b?


A. 2
B. 3
C. 5
D. 6
E. 8

The triangle inequality theorem states that

The length of any side of a triangle, b, is less than the sum of the lengths of the other two sides (c + a), and, simultaneously, is greater than the difference of the two (c - a)

Plain English: 1) Subtract one side from the other. Side \(b\) must be greater than that number; 2) Add the other two sides. Side \(b\) must be less than that number.

\((c-a)<\) third side, \(b < (c+a)\)

\(a=\frac{2}{3}\approx0.66\)
\(c=\frac{38}{8}=4.75\)

\((c-a) < b < (c+a)\)

\((4.75-0.66) < b < (4.75+0.66)\)

\(4.09<b<5.41\)

Given: side \(b\) is an integer
Only one integer lies in that range: \(b=5\)

Answer C
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If 2/3, 38/8 and b are sides of a triangle and b is an integer, what i &nbs [#permalink] 07 Sep 2018, 14:27
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