If 3 and 8 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?
I. 5
II. 8
III. 11
(A) ΙI only
(B) ΙII only
(C) I and ΙI only
(D) II and ΙII only
(E) I, ΙΙ, and ΙΙI
I'm confused how to set up the formulas here. Can any experts help?
If 3 and 8 are the lengths of two sides of a triangular regi
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THIRD-SIDE RULE:ardz24 wrote:If 3 and 8 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?
I. 5
II. 8
III. 11
(A) ΙI only
(B) ΙII only
(C) I and ΙI only
(D) II and ΙII only
(E) I, ΙΙ, and ΙΙI
In any triangle, the length of the third side must be less than the sum of the lengths of the other two sides and greater than the difference of the other two sides.
Let t = the third side of the triangle above.
Applying the third-side rule, we get:
8-3 < t < 8+3
5 < t < 11.
Thus, only II is a possible length for the third side.
The correct answer is A.
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IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .ardz24 wrote:If 3 and 8 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?
I. 5
II. 8
III. 11
(A) ΙI only
(B) ΙII only
(C) I and ΙI only
(D) II and ΙII only
(E) I, ΙΙ, and ΙΙI
difference between sides A and B < third side < sum of sides A and B
So, for this question: 8 - 3 < third side < 8 + 3
Simplify: 5 < third side < 11
So, the third side must be LONGER than 5 and SHORTER than 11
Answer: A
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Hi ardz24,ardz24 wrote:If 3 and 8 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?
I. 5
II. 8
III. 11
(A) ΙI only
(B) ΙII only
(C) I and ΙI only
(D) II and ΙII only
(E) I, ΙΙ, and ΙΙI
I'm confused how to set up the formulas here. Can any experts help?
Let's take a look at your question.
We are given with two sides of the triangle ans we need to choose the third one.
We know that sum of two sides of the triangle is always greater than the third side.
Using this rule we will choose the third side of the triangle.
Let's start with I. i.e. 5.
The sides of the triangle will be then 3, 8, 5
3 + 8 = 11 > 5
8 + 5 = 13 > 3
3 + 5 = 8, which is not greater than the third side i.e. 8.
It means, 5 can not be the third side of the triangle.
I.is not correct.
Let's check with II. i.e. 8.
The sides of the triangle will be then 3, 8, 8
3 + 8 = 11 > 8
8 + 8 = 16 > 3
3 + 8 = 11 > 8
It means, 8 can be the third side of the triangle.
II. is correct.
Let's check with III. i.e. 11.
The sides of the triangle will be then 3, 8, 11
3 + 8 = 11, which is not greater than the third side i.e. 11
It means, 11 can not be the third side of the triangle.
III. is not correct.
It means only II is correct.
Therefore, Option A is correct.
Hope this helps.
I am available if you'd like any follow up.
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In a pinch, the rule to remember:
|first side - second side| < third side < first side + second side
|first side - second side| < third side < first side + second side
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Since the sum of 2 of the sides of any triangle must be greater than the 3rd side, only 8 could be the length of the third side of the triangle.BTGmoderatorAT wrote: ↑Sun Sep 24, 2017 2:53 amIf 3 and 8 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?
I. 5
II. 8
III. 11
(A) ΙI only
(B) ΙII only
(C) I and ΙI only
(D) II and ΙII only
(E) I, ΙΙ, and ΙΙI
I'm confused how to set up the formulas here. Can any experts help?
Answer: A
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