Question

Question

Alisha wants to build a miniature bridge that will include a triangle made of wooden pieces. Which lengths of wood can she use to form a triangle? All lengths are given in inches.(1 point)
Responses

12, 16, and 28
12, 16, and 28

27, 12, and 16
27, 12, and 16

12, 4, and 16
12, 4, and 16

3, 16, and 12
3, 16, and 12
Skip to navigation

Answer 1

To determine which sets of lengths can form a triangle, we can use the Triangle Inequality Theorem. This theorem states that for any triangle with sides of length \( a \), \( b \), and \( c \), the following must hold true:

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

Let's check each set of lengths.

1. For lengths 12, 16, and 28:

   • \( 12 + 16 = 28 \) (not greater than 28)
   • This set cannot form a triangle.

2. For lengths 27, 12, and 16:

   • \( 12 + 16 = 28 > 27 \)
   • \( 12 + 27 = 39 > 16 \)
   • \( 16 + 27 = 43 > 12 \)
   • This set can form a triangle.

3. For lengths 12, 4, and 16:

   • \( 4 + 12 = 16 \) (not greater than 16)
   • This set cannot form a triangle.

4. For lengths 3, 16, and 12:

   • \( 3 + 12 = 15 < 16 \) (not greater than 16)
   • This set cannot form a triangle.

In conclusion, the only lengths that can form a triangle are 27, 12, and 16.