To determine the length of the third side of a 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 third side.
Since the first two sides measure 10 and 12, let's check which of the provided choices satisfy the triangle inequality theorem.
1) 10 + 12 > 30: This is true since 10 + 12 = 22 < 30. Therefore, 30 is not a valid length for the third side.
2) 10 + 12 > 15: This is true since 10 + 12 = 22 > 15. Therefore, 15 is a valid length for the third side.
3) 10 + 12 > 22: This is true since 10 + 12 = 22 = 22. Therefore, 22 is a valid length for the third side.
4) 10 + 12 > 24: This is true since 10 + 12 = 22 > 24. Therefore, 24 is not a valid length for the third side.
Thus, the valid lengths for the third side of the triangle are 15 and 22.
determine the length of the third side of a triangle from the choices provided if the first two sides measure 10 and 12
30
15
22
24
11 answers
Please pick 15 or 22
Based on the triangle inequality theorem, the valid lengths for the third side of the triangle are 15 or 22.
Its a one option only
Based on the triangle inequality theorem, the valid length for the third side of the triangle is 15.
two sides of a triangle measure 4 cm and 8 cm determine which of the following choices cannot be the measure of the third
8
6
5
10
8
6
5
10
To determine which of the provided choices cannot be the measure of the third side of the triangle, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Since the first two sides measure 4 cm and 8 cm, let's check which of the provided choices satisfy the triangle inequality theorem.
1) 4 + 8 > 8: This is true since 4 + 8 = 12 > 8. Therefore, 8 can be the measure of the third side.
2) 4 + 8 > 6: This is true since 4 + 8 = 12 > 6. Therefore, 6 can be the measure of the third side.
3) 4 + 8 > 5: This is true since 4 + 8 = 12 > 5. Therefore, 5 can be the measure of the third side.
4) 4 + 8 > 10: This is false since 4 + 8 = 12 is not greater than 10. Therefore, 10 cannot be the measure of the third side.
Thus, the measure of the third side of the triangle cannot be 10.
Since the first two sides measure 4 cm and 8 cm, let's check which of the provided choices satisfy the triangle inequality theorem.
1) 4 + 8 > 8: This is true since 4 + 8 = 12 > 8. Therefore, 8 can be the measure of the third side.
2) 4 + 8 > 6: This is true since 4 + 8 = 12 > 6. Therefore, 6 can be the measure of the third side.
3) 4 + 8 > 5: This is true since 4 + 8 = 12 > 5. Therefore, 5 can be the measure of the third side.
4) 4 + 8 > 10: This is false since 4 + 8 = 12 is not greater than 10. Therefore, 10 cannot be the measure of the third side.
Thus, the measure of the third side of the triangle cannot be 10.
apply the Traingle inewuality theroum and determine which option could be the third side of a triangle if the first two sides measure 4 and 8
1
2
9
11
1
2
9
11
To determine which option could be the measure of the third side of a triangle with the first two sides measuring 4 and 8, we need to apply 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 check each option:
1) 4 + 8 > 1: This is true since 4 + 8 = 12 > 1. Therefore, 1 could be the measure of the third side.
2) 4 + 8 > 2: This is true since 4 + 8 = 12 > 2. Therefore, 2 could be the measure of the third side.
3) 4 + 8 > 9: This is true since 4 + 8 = 12 > 9. Therefore, 9 could be the measure of the third side.
4) 4 + 8 > 11: This is false since 4 + 8 = 12 is not greater than 11. Therefore, 11 could not be the measure of the third side.
Based on the Triangle Inequality Theorem, options 1, 2, and 9 could be the measure of the third side of a triangle.
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 check each option:
1) 4 + 8 > 1: This is true since 4 + 8 = 12 > 1. Therefore, 1 could be the measure of the third side.
2) 4 + 8 > 2: This is true since 4 + 8 = 12 > 2. Therefore, 2 could be the measure of the third side.
3) 4 + 8 > 9: This is true since 4 + 8 = 12 > 9. Therefore, 9 could be the measure of the third side.
4) 4 + 8 > 11: This is false since 4 + 8 = 12 is not greater than 11. Therefore, 11 could not be the measure of the third side.
Based on the Triangle Inequality Theorem, options 1, 2, and 9 could be the measure of the third side of a triangle.
pick a single option
Based on the Triangle Inequality Theorem, the single option that could be the measure of the third side of a triangle with the first two sides measuring 4 and 8 is 9.
1 answer