Hello, magentarita!
In equilateral triangle $\displaystyle ABC$, $\displaystyle AB = 14$.
Find the perimeter of the triangle that joins the midpoints of the sides of $\displaystyle \Delta ABC.$ There is a theorem that says:
The line segment joining the midpoints of two side of a triangle
. . is parallel to and one-half the length of the third side. Code:
C
*
* *
* *
P *--------* Q
* *
* *
A * * * * * * * B
We have . $\displaystyle PQ \parallel AB,\quad \overline{PQ} \,=\,\frac{1}{2}(\overline{AB}) $
. . and this is true for any triangle.