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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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Joined: 02 Sep 2009
Posts: 50583
If 2/3, 38/8 and b are sides of a triangle and b is an integer, what i  [#permalink]

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04 Sep 2018, 23:30
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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 is b?

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

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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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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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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: $$b=5$$

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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