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# Which of the following describes all values of x such that there is a

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Math Expert
Joined: 02 Sep 2009
Posts: 64939
Which of the following describes all values of x such that there is a  [#permalink]

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22 May 2020, 05:52
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Difficulty:

5% (low)

Question Stats:

81% (00:41) correct 19% (01:07) wrong based on 52 sessions

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Which of the following describes all values of x such that there is a triangle with sides having lengths 3, 4, and x ?

A. 5 < x < 12
B. 4 < x < 7
C. 3 < x < 5
D. 1 < x < 7
E. 1 < x < 4

PS21256

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Which of the following describes all values of x such that there is a  [#permalink]

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22 May 2020, 05:56
2
Bunuel wrote:
Which of the following describes all values of x such that there is a triangle with sides having lengths 3, 4, and x ?

A. 5 < x < 12
B. 4 < x < 7
C. 3 < x < 5
D. 1 < x < 7
E. 1 < x < 4

PS21256

Property: FOr a triangle to exist, Sum if any two sides must be GREATER than third side

i.e. FOr $$x_{min}$$, 3+x > 4
i.e. $$x_{min} > 1$$

i.e. FOr $$x_{max}$$, 3+4 > x
i.e. $$x_{max} < 7$$

i.e. 1 < x < 7

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Which of the following describes all values of x such that there is a  [#permalink]

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22 May 2020, 10:05
Any side of a triangle is always between the (absolute sum and the absolute difference of the other two sides), exclusive.

|4 - 3| < x < |4 + 3|

So, 1 < x <7, Option D
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Re: Which of the following describes all values of x such that there is a  [#permalink]

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24 May 2020, 00:20
1
D.

Difference of two sides< third side < Sum of two sides
(4-3)<x< (4+3)
1<x<7
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Re: Which of the following describes all values of x such that there is a  [#permalink]

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25 May 2020, 07:09
Option D.

As per the property of Triangle, 4 - 3 < X < 4+3
1<X<7
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Re: Which of the following describes all values of x such that there is a  [#permalink]

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30 May 2020, 21:49

Solution

To find
We need to determine
• Which of the given Options describes all values of x, if there is a triangle with sides having lengths 3, 4, and x

Approach and Working out
• x must be < 3 + 4 and
• x must be greater than 4 – 3

Thus 1 < x < 7

Therefore, Option D is the correct answer.

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Re: Which of the following describes all values of x such that there is a   [#permalink] 30 May 2020, 21:49