### 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.

# Weighing the Baby

##### Stage: 4 Short Challenge Level:
See all short problems arranged by curriculum topic in the short problems collection

Weighing the baby at the clinic was a problem. The baby would not keep still and caused the scales to wobble. So I held the baby and stood on the scales while the nurse read off $78\;\mathrm{kg}$. Then the nurse held the baby while I read off $69\;\mathrm{kg}$. Finally I held the nurse while the baby read off $137\;\mathrm{kg}$. What was the combined weight of all three?

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.