### Building Tetrahedra

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

### Ladder and Cube

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.

# Weighing the Baby

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

Let $m$ be my weight, $b$ be the baby's weight and $n$ be the nurse's weight.

We have
\begin{align} m+b&=78\\ b+n&=69\\ m+n&=137\;. \end{align}
We can add all three equations together like this:
$$(m+b)+(b+n)+(m+n)=78+69+137\;.$$
It follows that $2(m+b+n)=284$ and hence $m+b+n=142$. So the combined weight is $142\;\mathrm{kg}$.

For an extra challenge can you find the weights of each person?

This problem is taken from the UKMT Mathematical Challenges.