### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Calendar Capers

Choose any three by three square of dates on a calendar page...

### 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...

# Intersecting Squares

##### Stage: 3 Short Challenge Level:
See all short problems arranged by curriculum topic in the short problems collection

Three congruent squares overlap as shown.

The areas of the three overlapping sections are $2\;\mathrm{cm}^2$, $5\;\mathrm{cm}^2$ and $8\;\mathrm{cm}^2$ respectively.

The total area of the non-overlapping parts of the squares is $117\;\mathrm{cm}^2$.

What is the side length of each square?

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.