Skip over navigation
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
Cat on a Wall
Age 14 to 16
ShortChallenge 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.
You may also like
Some(?) of the Parts
A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle
Triangle Midpoints
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
Fermat's Poser
Find the point whose sum of distances from the vertices (corners) of a given triangle is a minimum.