My (not so little) monkeys in KS3 have been discovering and using Pythagoras’ Theorem. They usually deal with open questions quite well, however this one took a fair bit of discussion. This challenge requires no worksheets or fancy resources, just write it on the board. The context is modified, but the essential question remains the same.

**Challenge**

Zookeepers have attached eight bolts in a cuboid formation (sides 3m, 4m and 5m) to the trees in a chimpanzee enclosure. The keepers attach taut ropes between the bolts for the chimps to climb on. Each length of rope is individually cut. No length is lost in knots.

- What is the maximum length of any one piece of rope?
- What is the total amount used, if every corner is joined without duplication?

**Solution**

The first step to solving it is a good diagram of the problem. Students then need to break it down into triangles. The solution has several levels of difficulty:

- Total of the edges of the cuboid
- Total of the diagonals on the faces
- Total of the diagonals across the inside of the cuboid

This diagram demonstrates the levels of the problem – have fun!

### Like this:

Like Loading...