### Tri.'s

How many triangles can you make on the 3 by 3 pegboard?

### Bracelets

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

### Tessellating Triangles

Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?

# Weekly Problem 8 - 2010

##### Stage: 2 and 3 Short Challenge Level:

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.

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