A lot of algebra involves deriving equations to represent problems and solving them. A very good example is found from geometry. The right angled triangle below has three unknown sides. Believe it or not, we can find the lengths of the sides knowing only the relationships shown between the lengths, and the fact that the triangle is right angled.
Because the triangle is right angled we can use theorems applicable to right angled triangles – specifically Pythagoras Theorem,
where c is the hypotenuse, the longest side. Label the sides
and
as below.
hence
or
is not plausible since a triangle cannot have negative lengths, so that