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
6cm
5cm
8cm
10cm
To determine which of the choices cannot be the measure of the third side, we can use 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, the two sides given are 4 cm and 9 cm. Let's check which of the following choices satisfies this condition:
6 cm: 4 + 6 > 9 (10 > 9) - Valid
5 cm: 4 + 5 > 9 (9 > 9) - Not valid
8 cm: 4 + 8 > 9 (12 > 9) - Valid
10 cm: 4 + 10 > 9 (14 > 9) - Valid
Therefore, the measure of the third side cannot be 5 cm. This is because the sum of the two given sides (4 cm and 5 cm) is not greater than the remaining side (9 cm).