Which type of triangle if any can be formed with sides measuring 8 inches, 8 inches, and three inches

Answer 1

To determine if a triangle can be formed with sides measuring 8 inches, 8 inches, and 3 inches, we can use the triangle inequality theorem. The theorem states that for any triangle with sides of lengths \( a \), \( b \), and \( c \), the following conditions must be satisfied:

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

Let’s assign the sides:

• \( a = 8 \)
• \( b = 8 \)
• \( c = 3 \)

Now we can check each condition:

1. \( 8 + 8 > 3 \) → \( 16 > 3 \) (True)
2. \( 8 + 3 > 8 \) → \( 11 > 8 \) (True)
3. \( 8 + 3 > 8 \) → \( 11 > 8 \) (True)

Since all three conditions are satisfied, a triangle can be formed with sides measuring 8 inches, 8 inches, and 3 inches.

Additionally, since two sides are equal (8 inches each), this triangle is an isosceles triangle.