To determine if a group of side measures will form a triangle, we need to apply 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 remaining side.
Let's apply the triangle inequality theorem to each group of side measures:
1) Group 1: 8, 1, 7
8 + 7 > 1
8 + 1 > 7
1 + 7 > 8
All three inequalities are true, so a triangle can be formed with side lengths 8, 1, and 7.
2) Group 2: 12, 10, 22
12 + 10 > 22
12 + 22 > 10
10 + 22 > 12
All three inequalities are true, so a triangle can be formed with side lengths 12, 10, and 22.
3) Group 3: 9, 4, 3
9 + 4 > 3
9 + 3 > 4
4 + 3 > 9
All three inequalities are true, so a triangle can be formed with side lengths 9, 4, and 3.
4) Group 4: 2, 7, 6
2 + 7 > 6
2 + 6 > 7
7 + 6 > 2
All three inequalities are true, so a triangle can be formed with side lengths 2, 7, and 6.
Therefore, all four groups of side measures will form triangles.
apply the triangle inequality theorem and etermine which group of side meaures will form a triangle
8, 1 7
12 10 22
9 4 3
2 7 6
5 answers
pick one
Let's pick Group 3: 9, 4, 3.
We will apply the triangle inequality theorem to this group:
9 + 4 > 3
9 + 3 > 4
4 + 3 > 9
All three inequalities are true, so a triangle can be formed with side lengths 9, 4, and 3.
We will apply the triangle inequality theorem to this group:
9 + 4 > 3
9 + 3 > 4
4 + 3 > 9
All three inequalities are true, so a triangle can be formed with side lengths 9, 4, and 3.
two sides of an triangle measure 3.7 and 8.2 apply the triangle inequality theorum to find a possible measure of the third sie.
3.5
4.5
4.2
5.5
3.5
4.5
4.2
5.5
To find a possible measure of the third side of a triangle with side lengths 3.7 and 8.2, we can apply 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 remaining side.
Let's apply the theorem to the given side lengths:
1) 3.7 + 8.2 > x (where x represents the unknown side length)
11.9 > x
2) 3.7 + x > 8.2
x > 4.5
3) x + 8.2 > 3.7
x > -4.5
Based on the inequality results, we can conclude that the possible measure of the third side (x) must be greater than 4.5 and less than 11.9.
Out of the options provided: 3.5, 4.5, 4.2, and 5.5, the only possible measure within the range is 4.5. Therefore, a possible measure for the third side is 4.5.
Let's apply the theorem to the given side lengths:
1) 3.7 + 8.2 > x (where x represents the unknown side length)
11.9 > x
2) 3.7 + x > 8.2
x > 4.5
3) x + 8.2 > 3.7
x > -4.5
Based on the inequality results, we can conclude that the possible measure of the third side (x) must be greater than 4.5 and less than 11.9.
Out of the options provided: 3.5, 4.5, 4.2, and 5.5, the only possible measure within the range is 4.5. Therefore, a possible measure for the third side is 4.5.