which of the following measurements is possible for the missing side le…

QUESTION IMAGE

Question

which of the following measurements is possible for the missing side length? select all that apply.

2
10
12
9
5
3

Explanation:

Response

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Apply the Triangle Inequality Theorem

Let the missing side length be \(x\).
\[

\begin{aligned} &6 - 4 < x < 6 + 4\\ &2 < x < 10 \end{aligned}

\]

Evaluate the given options

\[

\begin{aligned} &x = 2 \implies 2 < 2 \quad (\text{False})\\ &x = 10 \implies 10 < 10 \quad (\text{False})\\ &x = 12 \implies 12 < 10 \quad (\text{False})\\ &x = 9 \implies 2 < 9 < 10 \quad (\text{True})\\ &x = 5 \implies 2 < 5 < 10 \quad (\text{True})\\ &x = 3 \implies 2 < 3 < 10 \quad (\text{True}) \end{aligned}

\]
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Answer: