The middle line DF is drawn in the equilateral triangle ABC. Determine the perimeter of triangle FBD

| September 25, 2021 | education

The middle line DF is drawn in the equilateral triangle ABC. Determine the perimeter of triangle FBD if the side of the triangle is 14 cm.

1. The length of the midline of a triangle, parallel to one of the sides of the triangle, is half the length of this side. That is, DF = 1/2 AC = 14/2 = 7 centimeters.

2. The middle line DF of a triangle, according to its definition, connects the midpoints of two sides

AB and BC.

Therefore, AD = BD and BF = CF.

By the condition of the problem, the given triangle is equilateral, that is, all its sides are equal to 14 centimeters.

3. Therefore BD = BF = 14: 2 = 7 centimeters.

4. Calculate the perimeter of the triangle FBD (the total length of all its sides):

7 + 7 + 7 = 21 centimeters.

Answer: The perimeter of the FBD triangle is 21 centimeters.



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