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(( E )) is the midpoint of BC ,
Thus ;
[tex]BE = CE = 6[/tex]
So :
[tex]BC = 12[/tex]
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[tex] \frac{AC}{2} = DE \\ [/tex]
[tex] \frac{AC}{2} = 7.5 \\ [/tex]
Multiply sides by 2
[tex]2 \times \frac{AC}{2} = 2 \times 7.5 \\ [/tex]
[tex]AC = 15[/tex]
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[tex] \frac{AB}{2} = EF \\ [/tex]
[tex] \frac{AB}{2} = 8 \\ [/tex]
Multiply sides by 2
[tex]2 \times \frac{AB}{2} = 2 \times 8 \\ [/tex]
[tex]AB = 16[/tex]
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[tex]∆ABC \: \: Perimeter =
AB + BC + AC \\ [/tex]
[tex]
∆ABC \: \: Perimeter = 16 + 12 + 15 \\ [/tex]
[tex]
∆ABC \: \: Perimeter = 43[/tex]
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Done...
