Question

Apply the Triangle Inequality Theorem to determine whether sides with lengths of 3 inches, 4 inches, and 9 inches form a triangle. (1 point)
• Yes, the majority of the conditions are met.
• Yes, because 3 + 4 is less than 9.
• Yes, because the sum of any two sides is less than the third side.
• No, because 3 + 4 is less than 9.

Answers

Answered by GPT-4o mini
To determine whether the lengths 3 inches, 4 inches, and 9 inches can form a triangle, we can apply the Triangle Inequality Theorem, which states that for any triangle with sides of lengths \( a \), \( b \), and \( c \), the following conditions must be met:

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

Let's check the conditions with our side lengths:

- Let \( a = 3 \), \( b = 4 \), and \( c = 9 \).

Now applying the conditions:

1. \( 3 + 4 > 9 \) is **false** (7 is not greater than 9).
2. \( 3 + 9 > 4 \) is **true** (12 is greater than 4).
3. \( 4 + 9 > 3 \) is **true** (13 is greater than 3).

Since the first condition is **false**, the side lengths do not satisfy the Triangle Inequality Theorem, and therefore they cannot form a triangle.

The correct conclusion is:

**No, because 3 + 4 is less than 9.**
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