The longest side, five, is less than the sum of the two other sides (3+4=7). So, this is an example of the triangle inequality in action! What does this mean for the problem with sticks?…Age 7 to 11. Challenge Level.
| Number of sticks | Number of triangles |
|---|---|
| 8 | 1 |
| 9 | 3 |
| 10 | 2 |
| 11 | 4 |
How do you make 10 triangles with 5 popsicle sticks?
Expert Answers If you make a star with overlapping pieces this will create 10 triangles. There will be 5 on the outside and then 5 others on the inside.
How many different triangles can you make?
D. Given the three angles of a triangle, only ONE distinct triangle can be formed. We can use dilation to scale up or scale down and make an infinite number of triangle, based on this set of angles, all such triangles will be similar to each other.
How do you make a Star of David out of Popsicle sticks?
Paint the popsicle sticks and set aside to dry. Glue 3 sticks together to make a triangle and glue the other 3 sticks together to make a triangle. Let dry. Turn one of the triangles upside down (so the main point is pointing down) and glue over top of the other triangle to form the star.
Can we make a triangle with 6 matchsticks?
If you cannot make a triangle, think of reasons for it. This is an acute angle triangle and it is possible to make a triangle with the help of 6 matchsticks because sum of two sides is greater than third side.
How to calculate number of triangles possible with given lengths of sticks?
Approach: The main observation is that the triangles with area ≥ 0 can only be formed if there are three same lengths of sticks or one different and two similar lengths of sticks. Hence greedily iterate from the back and count the number of pairs of same length sticks available which is arr [i] / 2.
Can you make a triangle out of sticks?
If the length of a side used is more than half of the total number of sticks, this would not agree with the triangle inequality, and a triangle could not be made. Why not have a go at this to see for yourself to check you understand why the triangle inequality is true? Cong also spotted a general “rule”:
How many sticks do you need to make a table?
Cong from St Peter’s Roman Catholic School, Aberdeen was very thorough indeed, and sent in a fantastic solution to this problem. You must have worked very hard, Cong! Cong sent us a table of all the different triangles you can make with 4 sticks up to 20 sticks. Making a table was a very good idea.
Are there odd numbers that have more triangles than even numbers?
Odd numbers of seven and above always have more triangles than the even numbers adjacent to them. Odd numbers in the three times tables have even more as they have an equilateral triangle as well. In addition, Ellie, Emma, Olivia and Ibrahim from Lakeside looked at “rules” for being able to make equilateral triangles:
