If de = 37 cm and ef = 16 cm, then what are the possible lengths for df so that de, ef, and df can form a triangle? explain your reasoning.

21 < DF < 53 ; Triangle Inequality Theorem

Step-by-step explanation:

The Triangle Inequality Theorem states that the sum of any two sides is greater than the sum of the third side.

DE + EF > DF          EF + DF > DE                 DE + DF > EF

37 + 16 > DF           16 + DF > 37                  37 + DF > 16

       53 > DF                   DF > 21                           DF > -21

Now let's put together the answers.  Note that DF > -21 is irrelevant since all lengths must be greater than 0.

53 > DF  and DF > 21  means that DF is between 53 and 21

>    21 < DF < 53

you need to rotate this triangle about the origin 270 degrees clockwise to create the full square.