two sides of a triangle measure 4cm and 9cm. determine which of the following choices cannot be the measure of the third side
A. 10 cm
B. 5 cm
C. 8 cm
D. 6 sm
To determine which choice cannot be the measure of the third side of the triangle, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the two sides given are 4cm and 9cm. Let x be the length of the third side.
So, for option A:
4 + 9 > 10
13 > 10
This is true, so 10cm could be the length of the third side.
For option B:
4 + 9 > 5
13 > 5
This is true, so 5cm could be the length of the third side.
For option C:
4 + 9 > 8
13 > 8
This is true, so 8cm could be the length of the third side.
For option D:
4 + 9 > 6
13 > 6
This is also true, so 6cm could be the length of the third side.
Therefore, the answer is none of the choices cannot be the measure of the third side.