Can you solve it? The simple geometry question that fools almost everyone

Today’s two questions test your geometrical smarts. The first is about a triangle, the second about a square.

1. Tricky triangle

This one was sent in by a reader, aged 85, who first saw it in 1960. He is a roboticist who passed through Harvard, Princeton, Stanford and IBM. He says it is his favourite puzzle. ‘I’ve given this puzzle to perhaps 100 people. Over 80% have no idea how to solve it.’

What is the length of AD, the dashed line?

2. Rockin’ rectangles

This puzzle was sent in by reader David Stott, who devised it during lockdown.

It’s easy enough to divide a square into five rectangles.

But can you:

i) Divide a square into five rectangles such that no two rectangles share an entire side in common – i.e. the sides of abutting rectangles never start and finish at the same points? (The rectangles do not need to be the same size or shape.)

ii) Divide an 11 x 11 square into five rectangles in such a way that the ten side lengths are the whole numbers from 1 to 10? Hint: if you have solved part i) use this arrangement of rectangles.

I‘ll be back at 5pm UK with the solutions.

NO SPOILERS. Please discuss your favourite geometrical shapes

I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.