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What is the perimeter of a equilateral triangle inscribed in another equilateral triangle?

A side of an equilateral triangle is 10 cm. the mdpoints of its sides are joined to form an inscribed equilateral triangle... wat is the perimiter of the inscribed triangle? and how do u find it?

Public Comments

1. The perimeter of the inscribed triangle will be 15 cm. Joining the midpoints will create 4 congruent equilateral triangles with sides equal in length to 1/2 those of the original. To see this, remember that all of the angles of an equilateral triangle are equal to 60 degrees. When you join the midpoints, each of the smaller triangles formed at the vertices of the larger triangle are at least isosceles, since two of their sides must be 1/2 those of the original. The apex angle of each is 60 degrees, and the base angles opposite the equal sides must be equal, and the sum of all three is 180, so all three angles of each vertex sub-triangle must measure 60 degrees. Consequently, they are all equilateral. So all of their sides are equal to 5 cm, and that means the inscribed triangle which shares one side with each vertex triangle also has three sides of 5 cm. Q.E.D.
2. the inscribed equilateral triangle has side 5cm --->perimeter = 15cm