Given three side lengths, how many triangles can be formed?

Skip to content# Given three side lengths, how many triangles can be formed?

##
This Post Has 5 Comments

### Leave a Reply

Given three side lengths, how many triangles can be formed?

Given three side lengths, for example, a, b and c, you can form the triangle when

[tex]a+bc,\\ a+cb,\\ b+ca.[/tex]

If this property holds, then one triangle you can form. Each next triangle with the same sides lengths will be congruent to the first triangle by SSS postulate.

SSS postulate says: If the three sides of a triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

1 triangle, correct option is A.

We know that

In a triangle, the combined lengths of any two sides must always be greater than the length of the third side. (Triangle Inequality Theorem)

If all three side lengths are given and the combined length of two sides is greater than the length of the third side.

then

one unique triangle can be made

I believe the correct answer from the choices listed above is option 1. Given three side lengths, there would be 1 triangle that can be formed. For a given set of side length only one orientation of these lines that can be made.

Hope this answers the question. Have a nice day.

Given three side lengths, there would be 1 triangle that can be formed.

The answer would be 3 or 4 triangles.