Problem Solving

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?

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?

Hi ardz24,
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.

In a pinch, the rule to remember:

|first side - second side| < third side < first side + second side