Question

Which set of side lengths do NOT form a triangle? 2,3,5 Can 3 side lengtis form a A? X ▶0:00/2:46 D 3,5,7 5,7,10 6,14,18

Answer 1

To determine whether three side lengths can form a triangle, you can use the triangle inequality theorem, which states that for any triangle with sides of lengths \( a \), \( b \), and \( c \):

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

Now, let's check the given sets of side lengths:

1. **2, 3, 5:**
- \( 2 + 3 > 5 \) (5 is not greater than 5, so this fails)
- This set does NOT form a triangle.

2. **3, 5, 7:**
- \( 3 + 5 > 7 \) (8 > 7, true)
- \( 3 + 7 > 5 \) (10 > 5, true)
- \( 5 + 7 > 3 \) (12 > 3, true)
- This set forms a triangle.

3. **5, 7, 10:**
- \( 5 + 7 > 10 \) (12 > 10, true)
- \( 5 + 10 > 7 \) (15 > 7, true)
- \( 7 + 10 > 5 \) (17 > 5, true)
- This set forms a triangle.

4. **6, 14, 18:**
- \( 6 + 14 > 18 \) (20 > 18, true)
- \( 6 + 18 > 14 \) (24 > 14, true)
- \( 14 + 18 > 6 \) (32 > 6, true)
- This set forms a triangle.

Therefore, the only set of side lengths that does NOT form a triangle is **2, 3, 5**.