Answer:
The answer is [tex]\sqrt{105}[/tex] or approx. 10,25.
Step-by-step explanation:
[tex]EG^2=DG*GF \\ EG^2 = ab \\ EG = \sqrt{5*16} \\ EG = \sqrt{80}[/tex]
Now let's find EF.
[tex]EF^2 = GE^2+GF^2 \\ EF^2 = 80+256\\ EF=\sqrt{336}[/tex]
Now let's finally find DE.
[tex]DE = \sqrt{DF^2-EF^2} \\ DE = \sqrt{21^2-336} \\ DE = \sqrt{441-336} \\ DE=\sqrt{105}[/tex]
[tex]\sqrt{105} = 10,2469... = 10,25[/tex]
