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 8 cm 8 cm 6 cm 6 cm 10 cm 10 cm 5 cm

Answer 1

First, let's use the triangle inequality theorem to determine the range for the possible lengths of the third side.

According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let the three sides of the triangle be a, b, and c where a = 4 cm, b = 9 cm, and c is the unknown side length.

Now, we can determine the range for the possible values of c:

1. c < a + b
c < 4 + 9
c < 13

2. c > |a - b|
c > |4 - 9|
c > 5

Therefore, the third side must be greater than 5 cm and less than 13 cm.

Now, let's check the given choices:

1. 8 cm: 8 is in the range of 5 to 13, so it can be the measure of the third side.
2. 6 cm: 6 is in the range of 5 to 13, so it can be the measure of the third side.
3. 10 cm: 10 is in the range of 5 to 13, so it can be the measure of the third side.
4. 5 cm: 5 is not valid as it would violate the triangle inequality theorem.

Therefore, the measure that cannot be the measure of the third side of the triangle is 5 cm.