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..
To determine which choice cannot be the measure of the third side, we need to apply the triangle inequality theorem.
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.
In this case, we have two sides measuring 4 cm and 9 cm.
Thus, the third side must be greater than 9 - 4 = 5 cm, and less than 9 + 4 = 13 cm.
Therefore, any measure greater than or equal to 13 cm or less than or equal to 5 cm cannot be the measure of the third side.
Therefore, the only choice that cannot be the measure of the third side is 13 cm. The other choices (6 cm, 10 cm, and 5 cm) are within the possible range.