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Question 4 (1 point)
Given a triangle with sides of length 5 and 8, find the range of possible values for the third side. (Note: left
hand side of inequality in Blank 1 and right hand side in Blank 2)
Blank 1:
Blank 2:
____

Answer 1

3 < x < 13

Explanation:

Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Let x be the length of the unknown side.

Therefore, x will either be the longest side or one of the shorter sides.

Therefore:

x < 5 + 8

⇒ x < 13

And:

8 < 5 + x

⇒ 3 < x

So the range of possible values of the third side is greater than 3 and less than 13: 3 < x < 13