# Triangle inequality - practice 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.Direction: Solve each problem carefully and show your solution in each item.

#### Number of problems found: 28

- 3-bracket 2

Maybe the smallest angle in the triangle is greater than 70°? - Possible lengths

Find the possible lengths for the third side of a triangle with sides 20 and 18. - Triangles 8306

Find out how many triangles you create from lines 7 dm, 5 dm, 10 dm, 12 dm, and 15 dm long. - Triangle

By calculation, determine if it is possible to construct a triangle with sides 16 33 13. - Triangle

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

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

In an ABCD square, n interior points are chosen on each side. Find the number of all triangles whose vertices X, Y, and Z lie at these points and on different sides of the square. - Inequality 4434

The heel of height from the vertex C in the triangle ABC divides the side AB in the ratio 1:2. Prove that in the usual notation of the lengths of the sides of the triangle ABC, the inequality 3 | a-b | holds - Perimeter of a triangle

If the perimeter of a triangle is 6 2/3 cm and the lengths of two sides are 2 1/2 cm and 3 1/3 cm, find the length of the third side. - Following 64814

The two sides of the triangle have side lengths a = 6cm and b = 13cm. Then the following applies to the length of the third party c: (A) 7 - Triangles 80492

The sum of the lengths of the three segments is 140mm. Name at least 2 triplets of segment lengths from which we can construct a triangle. Construct triangles - 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 the triangle inequality). - Sin cos tan

In triangle ABC, right-angled at B. Sides/AB/=7cm, /BC/=5cm, /AC/=8.6cm. Find two decimal places. A. Sine C B. Cosine C C. Tangent C. - Perimeter 16663

The sizes of the sides of a triangle are three natural numbers. The two shorter sides have lengths a = 7 cm and b = 9 cm. What size will the third side be if we want the triangle to have the largest possible perimeter? - Exist triangle

Which of the following set of numbers could not represent the three sides of a triangle A. 13,22,34 B. 8,20,30 C. 10,14,23 D. 15,25,37 - 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? - Probability 3322

We have the numbers 4, 6, 8, 10, and 12. What is the probability that with a randomly selected triangle, these will be the lengths of the sides of a scalene triangle? - Probability 7991

We have the numbers 4, 6, 9, 13, and 15. What is the probability that these will be the lengths of the sides of the triangle? (Consider only scalene triangles.) - Triangle 71404

Which three lines of a given length can be three sides of a triangle? A / 42mm; 22mm; 12mm; B / 5cm, 50mm, 6cm; C / 10m, 5m, 50dm; D / 2.1cm, 4.2cm, 1.9cm - Equilateral 75284

Given are 6 line segments with lengths of 3 cm, 4 cm, 5 cm, 7 cm, 8 cm, and 9 cm. How many equilateral triangles can make from them? List all the options.

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