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Ladder and Cube
A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?
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Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.
Age 14 to 16 Short
Challenge Level
The ladder to a slide is 5 metres long, and the slide is 12 metres long. The ladder meets the slide at a right angle. This is shown in the diagram.
The distance along the ground from the bottom of the ladder to the bottom of the slide is 13 metres, as shown in the diagram.
How high off the ground is the top of the slide, to the nearest centimetre?
This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.