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.(1 point) Responses 5 cm 5 cm 8 cm 8 cm 6 cm 6 cm 10 cm
To determine which of the given choices cannot be the measure of the third side, we can use the triangle inequality theorem. This theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.
In this case, the two given sides measure 4 cm and 9 cm.
For the first choice, 5 cm, the sum of the two given sides is 4 + 5 = 9 cm, which is equal to the length of the third side. This follows the triangle inequality theorem, so this choice is possible.
For the second choice, 8 cm, the sum of the two given sides is 4 + 8 = 12 cm, which is greater than the length of the third side. This follows the triangle inequality theorem, so this choice is also possible.
For the third choice, 6 cm, the sum of the two given sides is 4 + 6 = 10 cm, which is equal to the length of the third side. This follows the triangle inequality theorem, so this choice is possible.
For the fourth choice, 10 cm, the sum of the two given sides is 4 + 10 = 14 cm, which is greater than the length of the third side. This follows the triangle inequality theorem, so this choice is also possible.
Therefore, the only remaining choice is 5 cm 5 cm 8 cm, which cannot be the measure of the third side.
there is only 1 digit for the answer
Apologies for the mistake. The correct answer is 10 cm. The sum of the two given sides (4 cm and 9 cm) is 4 + 9 = 13 cm, which is less than the length of the third side. According to the triangle inequality theorem, the third side must be greater than the sum of the other two sides. Therefore, 10 cm cannot be the measure of the third side.
wtf told you the answer is 10
Apologies for the confusion. Upon reevaluating, I made an error in my response. The correct answer is 5 cm.
The sum of the two given sides (4 cm and 9 cm) is 4 + 9 = 13 cm, which is greater than the length of the third side. 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 remaining side.
Therefore, the third side cannot be 5 cm, as it does not satisfy the triangle inequality theorem.