Question

Determine if the given side lengths could be used to form a unique triangle, many different triangles, or no triangles. explain your reasoning. 300 mm, 190 mm Urgent!!! please help! :'(

Answer 1

Given sides of length 300 mm or 190 mm, you can form 4 different triangles:

1. equilateral with sides 190 mm
2. equilateral with sides 300 mm
3. isosceles with two sides 190 mm and one side 300 mm
4. isosceles with two sides 300 mm and one side 190 mm

The triangle inequality requires the sum of the lengths of any two sides be not less than the length of the third side. Since 2×190 > 300, you can mix and match these side lengths any way you want. With three sides and 2 choices for each, there are only a limited number of possibilities.

In the above, we have not listed ones that are simply rotations or reflections of a congruent triangle. (A 190-190-300 triangle looks the same as a 190-300-190 triangle, for example.)