Given that G is the centroid of triangle AEC, the perimeter of triangle AEC is: A. 32 units
To understand how to derive the perimeter of [tex]\triangle AEC[/tex], recall the following related to centroid of a triangle in reference to the image in the attachment below:
- Medians of a triangle (i.e. AE, CD, and FB) connects the vertices (i.e. A, B & C) of a triangle to the midpoints (i.e. F, D, & E) of the opposite sides of the triangle.
- Centroid (i.e. O) is a point of concurrency of the triangle.
- By implication, all sides the triangle (i.e. AC, AB, & BC) are divided into two equal segments (i.e. FA= CF, AD = BD, & CE = BE)
Also, note that:
- Isosceles triangle have two equal sides (in triangle AEC given, EA = EC)
We're going to apply the above stated facts to solve the problem given since we are told that G is the centroid of the isosceles [tex]\triangle AEC[/tex]:
G = centroid (given)
AB = 6 units (given)
FA = 5 units (given)
EA = EC (equal sides of isosceles triangle)
EF = FA = 5 units
EA = EF + FA
EA = 5 + 5
EA = 10 units
EC = EA (equal sides of isosceles)
EC = 10 units
AB = CB = 6 units
AC = AB + CB
AC = 6 + 6
AC = 12 units
Perimeter of triangle AEC = AC + EA + EC
Perimeter of triangle AEC = 12 + 10 + 10 = 32 units
Therefore, given that G is the centroid of triangle AEC, the perimeter of triangle AEC is: A. 32 units
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