Determine the length of the third side of a triangle from the choices provided if the first two sides measure 10 and 12.
Pick one of the following choices.
1. 22
2. 15
3. 30
4. 24
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.
The measure of the third side must be less than the sum of the other two sides and greater than the difference of the other two sides.
Using this rule, we can eliminate choices that do not meet these criteria:
- 2 cm: Possible (9 - 4 < 2 < 9 + 4)
- 12 cm: Possible (9 - 4 < 12 < 9 + 4)
- 5 cm: Possible (9 - 4 < 5 < 9 + 4)
- 13 cm: Not possible (9 + 4 < 13)
Therefore, the answer is 13 cm.
According to the Triangle Inequality Theorem, the length of the third side of a triangle must be greater than the difference between the first two sides and smaller than the sum of the first two sides.
Using this rule, we can eliminate choices that do not meet these criteria:
1. 1 - Not possible (6 - 4 > 1)
2. 5 - Possible (6 - 4 < 5 < 6 + 4)
3. 8 - Possible (6 - 4 < 8 < 6 + 4)
4. 10 - Not possible (10 > 6 + 4)
Therefore, the possible options for the third side are 5 and 8.
Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.
The Triangle Inequality Theorem states that the length of any one side of a triangle must be less than the sum of the other two sides and greater than the difference between the other two sides.
To determine which group of side measures will form a triangle, we must apply this rule to each set of side measures:
1. 3 cm, 4 cm, 8 cm: Not possible (3 + 4 < 8)
2. 5 cm, 7 cm, 11 cm: Possible (5 + 7 > 11, 7 + 11 > 5, 11 + 5 > 7)
3. 2 cm, 3 cm, 9 cm: Not possible (2 + 3 < 9)
4. 6 cm, 8 cm, 16 cm: Not possible (6 + 8 < 16)
Therefore, the group of side measures that will form a triangle is 5 cm, 7 cm, and 11 cm.