Which set of side lengths will form a triangle? All measurements are in feet.(1 point) Responses 5, 3, 2 5, 3, 2 3, 6, 9 3, 6, 9 3, 7, 8 3, 7, 8 4, 1, 6

Answer 1

To determine if a set of side lengths can form a triangle, we can use the triangle inequality theorem. This theorem states that for any triangle with sides of lengths \( a \), \( b \), and \( c \), the following conditions must hold true:

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

Let's evaluate the sets of side lengths provided:

1. 5, 3, 2

   • \( 5 + 3 = 8 > 2 \) (True)
   • \( 5 + 2 = 7 > 3 \) (True)
   • \( 3 + 2 = 5 \not> 5 \) (False)

   This set cannot form a triangle.

2. 3, 6, 9

   • \( 3 + 6 = 9 \not> 9 \) (False)
   • This set cannot form a triangle.

3. 3, 7, 8

   • \( 3 + 7 = 10 > 8 \) (True)
   • \( 3 + 8 = 11 > 7 \) (True)
   • \( 7 + 8 = 15 > 3 \) (True)

   This set can form a triangle.

4. 4, 1, 6

   • \( 4 + 1 = 5 \not> 6 \) (False)
   • This set cannot form a triangle.

Based on the evaluations, the only set of side lengths that will form a triangle is 3, 7, 8.