Can three segments with length 4 cm, 6 cm, and 11 cm be assembled to form an acute triangle, a right triangle, or an obtuse triangle? Explain.

Three segments 4cm, 6cm, and 11cm cannot form a right triangle because if they could, then by Pythagorean theorem, 4^2 + 6^2 = 11^2, which is not true.

Moreover, the three segments cannot form an acute or obtuse triangle because by Triangle Inequality Theorem, the sum of two sides has to be greater than the third side. Here, (4cm + 6cm) is NOT larger than 11cm, and thus you cannot form a triangle.

joaobezerra joaobezerra · Answer 2 · 2021-11-04T11:11:33+01:00

Using triangle concepts, it is found that the sides with these lengths cannot form a triangle.

In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the larger side.

In this problem:

The smaller sides have lengths: 4 cm and 6 cm.
The larger side has length: 11 cm.

[tex]4 + 6 = 10 < 11[/tex]

Since the larger side length is greater than the sum of the lengths of the smaller sides, a triangle cannot be formed.

A similar problem is given at https://brainly.com/question/305520