Two sides of a triangle measure 4cm and 9cm. Determine which of the following choices CANNOT be the measure of the third side.
A. 8cm
B. 6cm
C.10cm
D.5cm
To determine which of the choices cannot be the measure of the third side, we can use the triangle inequality theorem.
The triangle inequality 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.
Let's denote the two sides of the triangle as 4cm and 9cm.
For the third side to be a triangle, the sum of the lengths of the two given sides (4cm and 9cm) must be greater than the length of the third side.
4cm + 9cm = 13cm
A. 8cm: 4cm + 8cm = 12cm (less than 13cm) - This can be the measure of the third side
B. 6cm: 4cm + 6cm = 10cm (less than 13cm) - This can be the measure of the third side
C. 10cm: 4cm + 10cm = 14cm (greater than 13cm) - This CANNOT be the measure of the third side
D. 5cm: 4cm + 5cm = 9cm (equal to 9cm) - This can be the measure of the third side
Therefore, the measure of 10cm (Choice C) CANNOT be the measure of the third side.