In the figure below, D is the midpoint of AB, E is the midpoint of BC, and F is the midpoint of AC. Find the perimeter of triangle ABC.
Answers
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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...
The perimeter of triangle ABC is 43.
The calculation is as follows:Since BE = CE = 6
So, BC = 12
Now
[tex]AC \div 2 = DE\\\\AC\div 2 = 7.5[/tex]
Now multiplied sides by 2
So,
[tex]2\times AC \div 2 = DE\\\\AC\div 2 = 7.5 \times 2[/tex]
AC = 15
Half of AB = EF
AB = 16
Now the perimeter is
= AB + BC + AC
= 16 + 12 + 15
= 43
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