The midsegment of a triangle divides the side lengths of the triangle into equal lengths.
The perimeter of triangle ABC is 36 units
Because the inner triangle forms the midsegment of the bigger triangle, then:
[tex]\mathbf{AB = DB}[/tex]
[tex]\mathbf{BE = EC}[/tex]
[tex]\mathbf{A F = FC}[/tex]
Where:
[tex]\mathbf{DB =6}[/tex]
[tex]\mathbf{FC =7}[/tex]
[tex]\mathbf{EC =5}[/tex]
So, we have:
[tex]\mathbf{AB = DB = 6}[/tex]
[tex]\mathbf{BE = EC = 5}[/tex]
[tex]\mathbf{A F = FC = 7}[/tex]
The perimeter of the triangle, is then calculated using:
[tex]\mathbf{Perimeter = AB + BC + AC}[/tex]
Split
[tex]\mathbf{Perimeter = AB+ DB + BE + EC + A F + FC}[/tex]
Substitute known values
[tex]\mathbf{Perimeter = 6+ 6+ 5+ 5+ 7+ 7}[/tex]
[tex]\mathbf{Perimeter = 36}[/tex]
Hence, the perimeter of triangle ABC is 36 units
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