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. 8
B. 6
C. 10
D. 5
D. 5
To determine if a side length can be the measure of the third side of a 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 given side lengths are 4 cm and 9 cm. Let x represent the measure of the third side.
4 + 9 > x
13 > x
Since the third side must be less than the sum of the other two sides, the third side must be less than 13 cm. Therefore, a side length of 5 cm cannot be the measure of the third side because it is not less than 13 cm.