Triangle Inequality Theorem Quick Check 1 of 51 of 5 Items Question Determine the length of the third side of a triangle from the choices provided if the first two sides measure 10 and 12.(1 point) Responses 15 15 24 24 30 30 22
To determine the length of the third side of a triangle when the first two sides measure 10 and 12, 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 third side.
In this case, the sum of the lengths of the two given sides is 10 + 12 = 22.
Therefore, the length of the third side must be greater than 22.
None of the provided choices are greater than 22, so none of them are correct.
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
6 cm
6 cm
8 cm
8 cm
10 cm.
To determine which of the following choices cannot be the measure of the third side of a triangle with side lengths 4 cm and 9 cm, we can use the Triangle Inequality Theorem. The 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. In other words, the third side must be shorter than the sum of the other two sides.
Let's consider each choice:
1) 5 cm: This is a possible length for the third side. (It is shorter than the sum of 4 cm and 9 cm, which is 13 cm.)
2) 6 cm: This is a possible length for the third side. (It is shorter than the sum of 4 cm and 9 cm, which is 13 cm.)
3) 8 cm: This is a possible length for the third side. (It is shorter than the sum of 4 cm and 9 cm, which is 13 cm.)
4) 10 cm: This is not a possible length for the third side. (It is equal to the sum of 4 cm and 9 cm, and the third side must be shorter.)
Therefore, the length that cannot be the measure of the third side is 10 cm.
now recheck you givin answer
Apologies for the incorrect response earlier. Let's recheck it:
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.
Given side lengths of 4 cm and 9 cm, we need to determine which of the following choices cannot be the measure of the third side:
1) 5 cm: The sum of 4 cm and 5 cm is 9 cm, which is greater than the other given side length of 9 cm. Therefore, 5 cm is a possible length for the third side.
2) 6 cm: The sum of 4 cm and 6 cm is 10 cm, which is greater than the other given side length of 9 cm. Therefore, 6 cm is a possible length for the third side.
3) 8 cm: The sum of 4 cm and 8 cm is 12 cm, which is greater than the other given side length of 9 cm. Therefore, 8 cm is a possible length for the third side.
4) 10 cm: The sum of 4 cm and 10 cm is 14 cm, which is greater than the other given side length of 9 cm. Therefore, 10 cm is a possible length for the third side.
Therefore, none of the provided choices (5 cm, 6 cm, 8 cm, 10 cm) cannot be the measure of the third side.