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Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

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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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Bendy Quad

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.

Perfectly Square

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Some experimentation with some integers might help.

The factorisation is not straight forward but the first and last terms are easy to establish, then the middle terms follow quite quickly.