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?

Correct answer:

n =  7

Step-by-step explanation:

$$\begin{gathered} a+b>c \\ {n}_1={\displaystyle \frac{5\cdot 4\cdot 3}{3\cdot 2}}=10 \\ 5>=2+3 \\ 6>=2+3 \\ 6>=2+4 \\ n=n_1-3=10-3=7 \end{gathered}$$

Try another example

Related math problems and questions:

• 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).
• Similarity coefficient
  In the triangle TMA the length of the sides is t = 5cm, m = 3.5cm, a = 6.2cm. Another similar triangle has side lengths of 6.65 cm, 11.78 cm, 9.5 cm. Determine the similarity coefficient of these triangles and assign similar sides to each other.
• Similar triangles
  The triangles ABC and XYZ are similar. Find the missing lengths of the sides of the triangles. a) a = 5 cm b = 8 cm x = 7.5 cm z = 9 cm b) a = 9 cm c = 12 cm y = 10 cm z = 8 cm c) b = 4 cm c = 8 cm x = 4.5 cm z = 6 cm
• Three-digit numbers
  How many three-digit numbers are from the numbers 0 2 4 6 8 (with/without repetition)?
• Similarity coefficient
  The ratio of similarity of two equilateral triangles is 3.5 (ie 7:2). The length of the side of smaller triangle is 2.4 cm. Calculate the perimeter and area of ​​the larger triangle.
• Divide
  How many different ways can three people divide 7 pears and 5 apples?
• 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?
• Combinations of sweaters
  I have 4 sweaters two are white, 1 red and 1 green. How many ways can this done?
• Rectangle - sides 4
  Perimeter of the rectangle is 72 cm. Calculate the length of the sides that are in the ratio 3:5.
• 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
• Similarity of two triangles
  The KLM triangle has a side length of k = 6.3cm, l = 8.1cm, m = 11.1cm. The triangle XYZ has a side length of x = 8.4cm, y = 10.8cm, z = 14.8cm. Are triangle KLM and XYZ similar? (write 0 if not, if yes, find and write the coefficient of a similarity)
• Permutations
  How many 4-digit numbers can be composed of numbers 1,2,3,4,5,6,7 if: and, the digits must not be repeated in the number b, the number should be divisible by 5 and the numbers must not be repeated c, digits can be repeated
• Similarity
  ABC is a triangle wherein a = 4 cm, b = 6 cm, c = 8 cm. Is it similar to the triangle DEF: d = 3 cm, e = 4.5 cm, f = 6 cm? If so, determine the ratio of similarity.
• Chess
  How many ways can select 4 fields on a classic chessboard with 64 fields so that fields don't have the same color?
• Tournament
  Determine how many ways can be chosen two representatives from 34 students to school tournament.
• In a
  In a triangle, the aspect ratio a: c is 3: 2, and a: b is 5: 4. The perimeter of the triangle is 74cm. Calculate the lengths of the individual sides.
• Five letters
  How many ways can five letters be arranged?