If all the faces of a tetrahedron have the same perimeter then show that they are all congruent.
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?
I keep three circular medallions in a rectangular box in which they
just fit with each one touching the other two. The smallest one has
radius 4 cm and touches one side of the box, the middle sized one
has radius 9 cm and touches two sides of the box and the largest
one touches three sides of the box. What is the radius of the
Clearly if $a$, $b$ and $c$ are the lengths of the sides of a
triangle and the triangle is equilateral then
$a^2 + b^2 + c^2 = ab + bc +
Is the converse true, and if so can you prove it? That is if
$a^2 + b^2 + c^2 = ab + bc + ca$ is the triangle with side lengths
$a$, $b$ and $c$ necessarily equilateral?