### 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?

### Areas and Ratios

What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.

# Near 10

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

We requre that $9< \sqrt {n}< 11$, or, equivalently, that $81< n< 121$.

Hence the possible integer values for n are the $39$ values $n = 82, 83,$ ... $, 119, 120$.

This problem is taken from the UKMT Mathematical Challenges.