Two sides of a triangle are 10 mm and 7 mm. using the Triangle Inequality Theorem (see picture above), determine the length of the third side from the choices given.
3 mm
3 mm
5 mm
5 mm
1 mm
1 mm
2 mm
2 mm
The third side must be greater than the difference between the other two sides, but less than the sum of the other two sides.
In this case, the third side must be greater than 10 - 7 = 3 mm, but less than 10 + 7 = 17 mm.
Therefore, the length of the third side must be 5 mm.
Two sides of a triangle are 6 in and 8 in. Using the Triangle Inequality Theorem (see picture above), which amount could be the length of the third side from the choices given?
10 in.
10 in.
2 in.
2 in.
1 in.
1 in.
The third side must be greater than the difference between the other two sides, but less than the sum of the other two sides.
In this case, the third side must be greater than 8 - 6 = 2 in, but less than 8 + 6 = 14 in.
Therefore, the length of the third side could be 10 in.
Using the Triangle Inequality Theorem (see picture above), determine which three sides of a triangle.
8, 8, 20
8, 8, 20
10, 20, 30
10, 20, 30
10, 15, 20
10, 15, 20
4, 8, 12
4, 8, 12
In a triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.
Let's apply this rule to each set of sides:
1. For sides 8, 8, 20: 8 + 8 is not greater than 20, so it does not form a triangle.
2. For sides 10, 20, 30: 10 + 20 is not greater than 30, so it does not form a triangle.
3. For sides 10, 15, 20: 10 + 15 is greater than 20, 10 + 20 is also greater than 15, and 15 + 20 is greater than 10. Therefore, this set of sides forms a triangle.
4. For sides 4, 8, 12: 4 + 8 is greater than 12, 4 + 12 is also greater than 8, and 8 + 12 is greater than 4. Therefore, this set of sides also forms a triangle.
So, the sets of sides that form triangles are:
- 10, 15, 20
- 4, 8, 12
Choose ONE please
Sure! Based on the Triangle Inequality Theorem, the three sides that form a triangle are 10, 15, 20.
Using the Triangle Inequality Theorem (see picture above), determine the length of the third side of the triangle. Side A is 10 m and side C is 12 m what is side B?
Side B equals 1 m
Side B equals 1 m
Side B equals 2 m
Side B equals 2 m
Side B equals 13 m
Side B equals 13 m
Based on 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.
So, for the sides A, B, and C where A = 10 m, C = 12 m, and we need to find B:
A + B > C
10 + B > 12
B > 2
Therefore, the length of Side B has to be greater than 2 m.
A + C > B
10 + 12 > B
22 > B
Therefore, the length of Side B has to be less than 22 m.
From the given choices, the only length that satisfies these conditions is:
Side B equals 13 m.
Fill in the blank to the correct response.
According to the Triangle Angle Sum Theorem, the sum of the inside angles of a triangle must be equal to _______
Responses.
90
90
100
100
180
180
360
360