### Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

### Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

# 3-sided

##### Stage: 4 Short Challenge Level:

Jack's teacher asked him to draw a triangle of area $7\textrm{ cm}^2$. Two sides are to be of length $6\textrm{ cm}$ and $8\textrm{ cm}$. How many possibilities are there for the length of the third side of the triangle?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
View the archive of all weekly problems grouped by curriculum topic