### Upsetting Pitagoras

Find the smallest integer solution to the equation 1/x^2 + 1/y^2 = 1/z^2

### Triangle Mid Points

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

### There and Back

Brian swims at twice the speed that a river is flowing, downstream from one moored boat to another and back again, taking 12 minutes altogether. How long would it have taken him in still water?

# Similar Rectangles

##### Stage: 3 and 4 Challenge Level:

The smaller of two similar rectangles has height $2$ units; the larger rectangle has length $6$ units.

If one rectangle has twice the area of the other, find the length of the smaller rectangle.

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from Tony Gardiner's 'Extension Mathematics Gamma' book.