Questions: 6,10, and 2 √34

6,10, and 2 √34
Transcript text: 6,10 , and $2 \sqrt{34}$
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Solution

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Solution Steps

Step 1: Identify the Given Lengths

The lengths provided are \( a = 6 \), \( b = 10 \), and \( c = 2\sqrt{34} \). Calculating \( c \) gives us approximately \( c \approx 11.6619 \).

Step 2: Apply the Triangle Inequality Theorem

To determine if these lengths can form a triangle, we check the following inequalities:

  1. \( a + b > c \)
  2. \( a + c > b \)
  3. \( b + c > a \)

Calculating each:

  1. \( 6 + 10 = 16 > 11.6619 \) (True)
  2. \( 6 + 11.6619 = 17.6619 > 10 \) (True)
  3. \( 10 + 11.6619 = 21.6619 > 6 \) (True)

Since all three conditions are satisfied, the lengths can indeed form a triangle.

Final Answer

The lengths \( 6 \), \( 10 \), and \( 2\sqrt{34} \) can form a triangle. Thus, the answer is \\(\boxed{\text{True}}\\).

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