# Triangle inequality - math problems

In any triangle, the sum of the lengths of any two sides is greater than the length of the remaining third one. The triangle inequality is three inequalities that are true simultaneously. The inequalities result directly from the triangle's construction. If one side were longer than two in total, the vertex against the longest side could not be constructed (or drawn), and the triangle as a shape in the plane would not exist.#### Number of problems found: 8

- Possible lengths

Find the most possible lengths for the third side of a triangle with sides 20 and 18. - 3-bracket 2

May be the smallest angle in the triangle greater than 70°? - Triangle

Prove whether you can construct a triangle ABC, if a=9 cm, b=6 cm, c=10 cm. - Right triangles

How many right triangles we can construct from line segments 3,4,5,6,8,10,12,13,15,17 cm long? (Do not forget to the triangle inequality). - Triangles

Five sticks with a length of 2,3,4,5,6 cm. How many ways can you choose three sticks to form three sides of a triangle? - The perimeter

The triangle has one side 5 cm long and the another 11 cm long. What can be the smallest and what is the largest perimeter? - Triangles

Hanka cut the 20 cm long straws into three pieces each piece had a length in cm. Then, with these three pieces, she tried to make a triangle. a) What circuit has each of the triangles? b) How long can the longest side measure? c) How many different triang - Triangles

Ivo wants to draw all the triangles whose two sides of which have a length of 4 cm and 9 cm, and the length of the third side is expressed in whole centimeters. How many triangles does he have?

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See also more information on Wikipedia.