Answer:
[tex]AB = 7\sqrt{21}\\CB= \sqrt{541}[/tex]
Step-by-step explanation:
Given: Δ ABC, CM⊥ AB
[tex]AC = 10, CM = 4 AM:BM = 2:5[/tex]
Now, consider [tex]AM:BM = 2:5 = 2x:5x[/tex]
Let In ΔCMA H=- 10 , P= 4 , B= 2x
By, Pythagoras theorem, [tex]H^2=P^2+B^2[/tex]
putting values we get, [tex]10^2=4^2+(2x)^2[/tex]
⇒ [tex]100=16+4x^2[/tex]
⇒[tex]x^2= 21[/tex]
⇒[tex]x= \sqrt{21}[/tex]
which gives us [tex]AM = 2x= 2\sqrt{21}[/tex] and [tex]MB = 5x= 5\sqrt{21}[/tex]
⇒[tex]AB= 2\sqrt{21}+5\sqrt{21}[/tex]
⇒[tex]AB= 7\sqrt{21}[/tex]
Now, Let In ΔCMB H=- ? , P= 4 , B= 5√21
By, Pythagoras theorem, [tex]H^2=P^2+B^2[/tex]
putting values we get, [tex]H^2=4^2+(5\sqrt{21})^2[/tex]
⇒ [tex]H^2=16+525[/tex]
⇒[tex]H^2=541 [/tex]
⇒[tex]H= \sqrt{541}[/tex]
⇒ [tex]CB= \sqrt{541}[/tex]
Therefore, [tex]AB = 7\sqrt{21}\\CB= \sqrt{541}[/tex]
