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Building Tetrahedra

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

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Rudolff's Problem

A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?

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Three circular medallions fit in a rectangular box. Can you find the radius of the largest one?


Stage: 4 Challenge Level: Challenge Level:1
Try some numerical examples and then just use elementary algebra. You will need to be able to handle algebraic fractions and to do a simple factorisation.