This diagram shows how to construct a 3:4:5 triangle by inscribing certain diagonals in a square of area 20.

Another way of making a 3-4-5 triangle is to take three discs, of radii 1, 2, and 3, and place them so they are mutually tangential. The centres of the discs are then at the vertices of the triangle:

(In general, to make a triangle with sides a, b, c, you need discs with radii (b+c-a)/2, (a+c-b)/2, (a+b-c)/2.)

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