Answer:
DF) = 10
AB) = 5
EF) = 12.5
Step-by-step explanation:
For length AB
[tex]3^{2} +4^{2} = AB^{2}[/tex] -> 9+16=[tex]\sqrt{25}[/tex] -> 5
For length DF
We know that AD is 2.5 times smaller than DE (7.5 / 3)
Now we can use that to determine length DF
BD = 4, DF = 4*2.5 = 10
using the Pythagorean theorem, you can find EF:
[tex]DE^{2} +DF^{2} =EF^{2}[/tex]
[tex]7.5^{2}+ 10^{2} =12.5[/tex]
