HOW HOW YOU KNOW if the three engths can form a triangle. $$ 3,9,8 $$ True False

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UpStudy AI · Accepted Answer

To determine if three lengths can form a triangle, we can use the triangle inequality theorem. This theorem states that for any three lengths $$ a $$, $$ b $$, and $$ c $$, the following conditions must be satisfied:

1. $$ a + b > c $$
2. $$ a + c > b $$
3. $$ b + c > a $$

In this case, the lengths are $$ 3 $$, $$ 9 $$, and $$ 8 $$. Let's denote them as follows:
- $$ a = 3 $$
- $$ b = 9 $$
- $$ c = 8 $$

Now, we will check the three conditions:

1. $$ a + b > c $$: 
   $$
   3 + 9 > 8 \quad \Rightarrow \quad 12 > 8 \quad \text{(True)}
   $$

2. $$ a + c > b $$: 
   $$
   3 + 8 > 9 \quad \Rightarrow \quad 11 > 9 \quad \text{(True)}
   $$

3. $$ b + c > a $$: 
   $$
   9 + 8 > 3 \quad \Rightarrow \quad 17 > 3 \quad \text{(True)}
   $$

Since all three conditions are satisfied, the lengths $$ 3 $$, $$ 9 $$, and $$ 8 $$ can indeed form a triangle.

Thus, the answer is **True**.
The lengths 3, 9, and 8 can form a triangle because they satisfy the triangle inequality theorem.

HOW HOW YOU KNOW if the three engths can form a triangle. \[ 3,9,8 \] True False

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