Question

ASAP PLEASE HELP.

Choose a real world object that you can cut into three different lengths to form a triangle. Find three side lengths that form a triangle and three lengths that do not form a triangle. For each triangle, give the side lengths and explain why those lengths do or do not form triangle. Triangle 1: ____________________________. Triangle 2: _________________________________.​

Answer 1

One real-world object that can be cut into three different lengths to form a triangle is a piece of rope.

Triangle 1: Side lengths 3 cm, 4 cm, and 5 cm. These lengths form a triangle because they satisfy the triangle inequality theorem, where 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, 3 + 4 > 5, 3 + 5 > 4, and 4 + 5 > 3.

Triangle 2: Side lengths 2 cm, 5 cm, and 8 cm. These lengths do not form a triangle because they violate the triangle inequality theorem. For example, 2 + 5 < 8, so it’s not possible to form a triangle with these lengths since one side would be longer than the sum of the other two sides.