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Cat on a Wall

Age 14 to 16 Short
Challenge Level

A cat lies on top of a low wall and looks up towards the birds in the top of a tree. There is a bush between the cat and the tree, and the cat can only just see over the top of the bush.

The bush is a horizontal distance of H metres from the wall, and the tree is a horizontal distance of H metres from the bush.

The height of the bush is 4 m. The height of the tree is 7 m.

How high is the wall?

This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.