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# geometric question

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What is the range of possible sizes for side x?

Aug 31, 2020

### 2+0 Answers

#1
+1039
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Using the triangle inequality theorem, we can form these inequalities:

8 + 8.8 > x

8 + x > 8.8

x + 8.8 > 8

We technically don't need the third one, because we already know that x is greater than -0.8. (because lengthes can't be negative)

8 + 8.8 > x

8 + x > 8.8

We now need to isolate the "x" in the second inequality:

x > 8.8 - 8

x > 0.8

Here is what we now know about x:

x < 16.8

x > 0.8

Therefore, the range for x is: {x | 0.8 < x < 16.8 }

EXTRA KNOWLEDGE:

This is not needed, but the range in interval notation form is (0.8, 16.8)

EDIT: Sorry, I used the wrong numbers!

:)

Aug 31, 2020
edited by ilorty  Aug 31, 2020
#2
+10597
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What is the range of possible sizes for side x?

Hello Guest!

$$x \in \{\mathbb{R}\ |0.8 < x < 16.8 \}$$

!

Aug 31, 2020
edited by asinus  Aug 31, 2020