Triangle inequality theorem quick check

Question

Apply the triangle inequality theorem to determine whether sides with lengths of 4 inches, 8 inches and 9 inches form a triangle

Answer 1

To determine whether the lengths of 4 inches, 8 inches, and 9 inches can form a triangle using the triangle inequality theorem, we need to check the following three conditions:

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

Let's assign the sides:

• \( a = 4 \)
• \( b = 8 \)
• \( c = 9 \)

Now, we'll check each condition:

1. \( 4 + 8 > 9 \)

   • \( 12 > 9 \) (True)

2. \( 4 + 9 > 8 \)

   • \( 13 > 8 \) (True)

3. \( 8 + 9 > 4 \)

   • \( 17 > 4 \) (True)

Since all three conditions are satisfied, the lengths of 4 inches, 8 inches, and 9 inches can indeed form a triangle.