To determine which choices cannot be the measure of the third side of the triangle, we will use the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's consider the sides of length 4 cm and 9 cm:
1) If the third side is 1 cm, the sum of the lengths of the two known sides is 4 cm + 9 cm = 13 cm. However, 13 cm is greater than 1 cm, so this option is valid.
2) If the third side is 2 cm, the sum of the lengths of the two known sides is 4 cm + 9 cm = 13 cm. However, 13 cm is greater than 2 cm, so this option is valid.
3) If the third side is 3 cm, the sum of the lengths of the two known sides is 4 cm + 9 cm = 13 cm. However, 13 cm is greater than 3 cm, so this option is valid.
4) If the third side is 4 cm, the sum of the lengths of the two known sides is 4 cm + 9 cm = 13 cm. However, 13 cm is equal to 4 cm, so this option is not valid.
5) If the third side is 5 cm, the sum of the lengths of the two known sides is 4 cm + 9 cm = 13 cm. 13 cm is greater than 5 cm, so this option is valid.
Based on the triangle inequality theorem, the lengths of the sides cannot exceed or equal the sum of the lengths of the other two sides. Therefore, the third side cannot measure 4 cm as it would violate the triangle inequality theorem.
Two sides of a triangle measure four centimeters and nine centimeters determined which the following choices cannot be the measure of the third side
1 answer