posted by Jt
Draw a circle with 5cm radius. Inscribe a triangle with side ratio 5:6:7 in it.
so, draw the circle. The central angles subtended by the sides will be 100,120,140 degrees. It is easy to construct a 120° angle, so you can draw the side of length 6x first. Then from its ends draw arcs of radius 5x and 7x. They will intersect at the third vertex.
I got that wrong. The angles are not in the same ratio as the sides. The sines of the angles are.
So, you can still draw the triangle, but then you need to circumscribe it.
You can easily find online the relationship between the radius and the sides. In this case, with sides of 5,6,7 the radius is 35/(4√6) so just scale the sides appropriately.