Question

3 connecting lines are shown. Line D F is horizontal. Line D E is about half the length of line D F. Line F E is about one-third of the length of line D F.

Which inequality explains why these three segments cannot be used to construct a triangle?

EF + FD > DE
ED + EF < DF
ED + EF > DF
EF + FD < DE

Answer 1

ED + EF < DF or b

Answer 2

second option ED + EF < DF

Explanation:

in order to build a triangle or of 3 lines, every pair of 2 of these lines must be longer together than the third line.

otherwise you could put them together and place them flat alongside the third line and still cannot connect to the endpoint of the third line => no triangle possible.

ED (or DE) is half of the third line (DF or FD).

FE (or EF) is a third of the third line.

1/2 + 1/3 < 1/1 (because 1/3 < 1/2)