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
22
22
15
15
24
24
30
To determine the length of the third side of a 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.
In this case, the first two sides measure 10 and 12. To determine the possible range of values for the third side, we can add and subtract these two values:
10 + 12 = 22
12 - 10 = 2
Therefore, the third side must be greater than 2 units and less than 22 units.
Among the choices provided, the closest value within this range is 15.
Thus, the length of the third side is 15.
To determine which of the choices cannot be the measure of the third side, 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.
In this case, the two given sides measure 4 cm and 9 cm. Let's consider each choice and see if it satisfies the triangle inequality theorem:
1) 6 cm: 4 + 6 = 10, which is greater than 9. This can be the measure of the third side.
2) 5 cm: 4 + 5 = 9, which is equal to 9. This can be the measure of the third side, but it would form a degenerate triangle (a straight line) with the two given sides.
3) 10 cm: 4 + 10 = 14, which is greater than 9. This can be the measure of the third side.
4) 8 cm: 4 + 8 = 12, which is greater than 9. This can be the measure of the third side.
From these calculations, it can be concluded that the third side cannot measure 5 cm.
so whats the answers for the entire thing
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
6 cm
6 cm
5 cm
5 cm
10 cm
10 cm
8 cm
Apply the Triangle Inequality Theorem and determine which option could be the third side of a triangle if the first two sides measure 4 and 6.(1 point)
Responses
9
9
1
1
11
11
2
Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.
Responses
9, 4, 3
9, 4, 3
8, 1, 7
8, 1, 7
12, 10, 22
12, 10, 22
2, 7, 6
2, 7, 6
To apply the Triangle Inequality Theorem and determine which option could be the third side of a triangle, we need to check if the sum of the lengths of the first two sides is greater than the length of the third side.
In this case, the first two sides measure 4 and 6. Let's check each option:
1) 9: 4 + 6 = 10, which is greater than 9. So, 9 could be the length of the third side.
2) 1: 4 + 6 = 10, which is greater than 1. So, 1 could be the length of the third side.
3) 11: 4 + 6 = 10, which is less than 11. So, 11 could not be the length of the third side.
4) 2: 4 + 6 = 10, which is not greater than 2. So, 2 could not be the length of the third side.
From these calculations, it can be concluded that the third side could be either 9 or 1.