Two sides of a triangle measure 4 cm and 9 cm determine which of the following choices cannot be measured side a 10 cm B6 CM 8 cm d5 cm
To determine which side lengths are impossible for the third side of the 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 remaining side.
Let's apply this theorem to each option:
A) Side lengths of 4 cm, 9 cm, and 10 cm:
Using the triangle inequality theorem, we have 4 cm + 9 cm > 10 cm. This is true, so option A is possible.
B) Side lengths of 4 cm, 9 cm, and 6 cm:
Using the triangle inequality theorem, we have 4 cm + 6 cm > 9 cm. This is true, so option B is possible.
C) Side lengths of 4 cm, 9 cm, and 8 cm:
Using the triangle inequality theorem, we have 4 cm + 8 cm > 9 cm. This is true, so option C is possible.
D) Side lengths of 4 cm, 9 cm, and 5 cm:
Using the triangle inequality theorem, we have 4 cm + 5 cm > 9 cm. This is false, as 9 cm is not greater than 9 cm. Therefore, option D is not possible.
Therefore, the answer is option D - a side length of 5 cm cannot be measured.