For each sets of lengths determine if it is possible or not to form a triangle:
1) AB = 4 cm, BC = 6 cm, AC = 12 cm
2) AB = 2 cm, BC = 8 cm, AC = 5 cm
if the sum of the two smaller sides is ≤ the largest side
... a triangle cannot be made (won't close up)
actually, the largest side must be less than the sum of the two smallest sides.
To determine if it is possible to form a triangle with the given sets of lengths, we need to apply the Triangle Inequality Theorem.
According to 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.
Let's analyze each set of lengths separately:
1) AB = 4 cm, BC = 6 cm, AC = 12 cm
To check if it is possible to form a triangle, we need to verify if the sum of any two sides is greater than the third side.
- AB + BC = 4 cm + 6 cm = 10 cm (which is less than AC)
- BC + AC = 6 cm + 12 cm = 18 cm (which is greater than AB)
- AC + AB = 12 cm + 4 cm = 16 cm (which is greater than BC)
Since, for this set of lengths, the sum of any two sides is not greater than the length of the third side, it is NOT possible to form a triangle.
2) AB = 2 cm, BC = 8 cm, AC = 5 cm
Let's apply the Triangle Inequality Theorem to this set:
- AB + BC = 2 cm + 8 cm = 10 cm (which is greater than AC)
- BC + AC = 8 cm + 5 cm = 13 cm (which is greater than AB)
- AC + AB = 5 cm + 2 cm = 7 cm (which is less than BC)
Since, for this set of lengths, the sum of any two sides is greater than the length of the third side, it is possible to form a triangle.
In conclusion:
1) It is NOT possible to form a triangle with the lengths 4 cm, 6 cm, and 12 cm.
2) It is possible to form a triangle with the lengths 2 cm, 8 cm, and 5 cm.