Question

which choice shows three lengths that cannot be the lengths of the three sides of a triangle? (choose 2 answers)


A. 2,4,7
B. 3,10,10
C. 3,6,12
D. 4,8,10

Answer 1

To determine which choices cannot form the lengths of 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 inequalities must hold true:

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

We will apply this to each choice.

**A. 2, 4, 7**
- Check: \(2 + 4 = 6\) which is not greater than \(7\).
- This does not satisfy the triangle inequality. **(This choice cannot form a triangle)**

**B. 3, 10, 10**
- Check: \(3 + 10 = 13 > 10\)
- Check: \(3 + 10 = 13 > 10\)
- Check: \(10 + 10 = 20 > 3\)
- All conditions are satisfied. **(This choice can form a triangle)**

**C. 3, 6, 12**
- Check: \(3 + 6 = 9\) which is not greater than \(12\).
- This does not satisfy the triangle inequality. **(This choice cannot form a triangle)**

**D. 4, 8, 10**
- Check: \(4 + 8 = 12 > 10\)
- Check: \(4 + 10 = 14 > 8\)
- Check: \(8 + 10 = 18 > 4\)
- All conditions are satisfied. **(This choice can form a triangle)**

In summary, the two choices that cannot form the lengths of a triangle are:

- **A. 2, 4, 7**
- **C. 3, 6, 12**