DEF is an isosceles triangle. DF – base, EC – median. The perimeter of triangle DEF is 35

DEF is an isosceles triangle. DF – base, EC – median. The perimeter of triangle DEF is 35 cm and the perimeter of triangle CEF is 30 cm.Find the length of the median EC

Let’s take a simple solution. Since the given triangle DEF is isosceles, the median EC halves not only the base of DF, but also the entire triangle in half. Hence, we can safely say that the median EC divides the perimeter of the triangle DEF in half, i.e. 35: 2 = 17.5. From the problem statement, the perimeter of the triangle CEF is 30 cm, where EC is the median. We also know the two sides of the triangle CEF, EF + CF = 17.5. Obviously EC = 30 – (EF + CF) = 30 – 17.5 = 12.5. We found the median EC = 12.5 cm.