Question

Question

The following side lengths, in meters, were given to a carpenter to build a front porch with a triangular design. The carpenter needs to determine which set of lengths will make a triangle to be able to use it in his design. (Hint: Use the Triangle Inequality Theorem)
Option 1: Side lengths: 3, 3, 6
Option 2: Side lengths: 6, 8, 10
Option 3: Side lengths: 4, 6, 13(1 point)
Responses

Option 1
Option 1

Option 2
Option 2

Option 3

Answer 1

To determine which set of side lengths can form a triangle, we can use the Triangle Inequality Theorem. The theorem states that for any triangle with sides of length \( a \), \( b \), and \( c \), the following conditions must be met:

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

Let's check each option:

Option 1: Side lengths: 3, 3, 6

• Check: \( 3 + 3 > 6 \) (6 is not greater than 6, so it fails)
• Conclusion: These lengths cannot form a triangle.

Option 2: Side lengths: 6, 8, 10

• Check: \( 6 + 8 > 10 \) (14 > 10, valid)
• Check: \( 6 + 10 > 8 \) (16 > 8, valid)
• Check: \( 8 + 10 > 6 \) (18 > 6, valid)
• Conclusion: These lengths can form a triangle.

Option 3: Side lengths: 4, 6, 13

• Check: \( 4 + 6 > 13 \) (10 is not greater than 13, so it fails)
• Conclusion: These lengths cannot form a triangle.

Based on the checks, the only option that can form a triangle is Option 2: Side lengths: 6, 8, 10.