How many triangles can you make on the 3 by 3 pegboard?
Investigate the different shaped bracelets you could make from 18
different spherical beads. How do they compare if you use 24 beads?
Can you make these equilateral triangles fit together to cover the
paper without any gaps between them? Can you tessellate isosceles
A triangle $T$ has an area of $1$cm$^2$. Let $M$ be the product of the perimeter of $T$ and the sum of the three altitudes of $T$. Which of the following statements is false?
A. There are (or there exist) triangles $T$ for which $M> 1000$
B. $M> 6$ for all triangles $T$
C. There are triangles $T$ for which $M=18$
D. $M> 16$ for all right-angled triangles
E. There are triangles $T$ for which $M< 12$
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.