Question

How many triangles can be constructed with sides measuring 15 cm, 7 cm, and 5 cm?
Responses

more than one
more than one

none
none

one

Answer 1

To determine how many triangles can be formed with sides measuring 15 cm, 7 cm, and 5 cm, we can use the triangle inequality theorem. This theorem states that for any triangle with sides \(a\), \(b\), and \(c\), the following conditions must hold true:

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

Let's assign the sides:
- \(a = 15\) cm
- \(b = 7\) cm
- \(c = 5\) cm

Now, we will check the triangle inequalities:

1. \(15 + 7 > 5\) → \(22 > 5\) (True)
2. \(15 + 5 > 7\) → \(20 > 7\) (True)
3. \(7 + 5 > 15\) → \(12 > 15\) (False)

Since the third condition fails, the sides do not satisfy the triangle inequality. Therefore, it is impossible to form a triangle with these side lengths.

**The answer is: none.**