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.
a: 5 cm
b: 8 cm
c: 6 cm
d: 10 cm
To determine which choice cannot be the measure of the third side, we need to use the triangle inequality theorem. The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
For the given triangle, the two sides that we know the measures of are 4 cm and 9 cm.
Let's check each choice against the triangle inequality theorem:
a: 5 cm
4 cm + 5 cm = 9 cm
9 cm > 5 cm
This means that 5 cm could be the measure of the third side.
b: 8 cm
4 cm + 8 cm = 12 cm
12 cm > 9 cm
This means that 8 cm could be the measure of the third side.
c: 6 cm
4 cm + 6 cm = 10 cm
10 cm > 9 cm
This means that 6 cm could be the measure of the third side.
d: 10 cm
4 cm + 10 cm = 14 cm
14 cm > 9 cm
This means that 10 cm could be the measure of the third side.
None of the choices violate the triangle inequality theorem, so all of them could be the measure of the third side. Therefore, the correct answer is none of the above.