Question

Can a triangle be made with sides of length seven, 10, 20

Answer 1

No, a triangle can't be made with sides of those lengths.

-- The 10 and the 20 must be hooked together somewhere on the triangle.
One end of the 10 is connected to one end of the 20.

-- Now imagine the distance between the OTHER ends of those sides.
If the 10 and the 20 are folded together so that they both go in the same
direction and there's no angle between them, the closest their OTHER ends
can be is 10 units apart.

-- So if you want to stick a 3rd side between them and make a triangle,
the 3rd side has to be AT LEAST 10 units long.  If it's any shorter than
10 units, it can't reach the open ends of the 10 and the 20.

--  Seven is less than 10.
So it can't reach the open ends of both the 10 and the 20 at the same time.