Question

Two sides of a triangle measure 4 cm and 9 cm. Determine which of the following choices cannot be the measure of the third side.(1 point)
Responses

10 cm
10 cm

6 cm
6 cm

5 cm
5 cm

8 cm

Pls be right

Answer 1

To determine which length cannot be the measure of the third side of a triangle when the other two sides are 4 cm and 9 cm, we can use the triangle inequality theorem. The triangle inequality states that for any triangle with sides of lengths \( a \), \( b \), and \( c \):

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

Let the sides be:
- \( a = 4 \) cm
- \( b = 9 \) cm
- \( c \) is the length of the third side.

Now apply the triangle inequality:

1. \( 4 + 9 > c \)
- This simplifies to \( c < 13 \).

2. \( 4 + c > 9 \)
- This simplifies to \( c > 5 \).

3. \( 9 + c > 4 \)
- This simplifies to \( c > -5 \) (always true for positive lengths).

So the conditions we have are:
- \( c < 13 \)
- \( c > 5 \)

This means the possible values for the third side \( c \) must satisfy:
\[ 5 < c < 13 \]

Now let's examine the provided options:
- **10 cm**: Valid (since \( 5 < 10 < 13 \))
- **6 cm**: Valid (since \( 5 < 6 < 13 \))
- **5 cm**: Not Valid (since \( 5 \) is not greater than \( 5 \))
- **8 cm**: Valid (since \( 5 < 8 < 13 \))

Thus, the third side cannot be **5 cm**.