In a △ABC, D, E and F are the mid-points of side BC, CA and AB respectively. If BC = 25.6 cm. CA = 18.8 cm and AB = 20.4 cm, what is the perimeter (in cm) of the △DEF?

32.4

In a ΔABC,

BC = 25.6 cm,

CA = 18.8 cm and AB = 20.4 cm

We have a concept,

The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.

Here,

E and F are the mid point of the side AC and AB 

\(\frac{ AE }{EC}\) = \(\frac{ AF }{FB}\)

By mid point theorem,

= EF = \(\frac{ BC }{2}\) = \(\frac{ 26.6 }{2}\)

= EF = 12.8 cm

Similarly,

DE = \(\frac{ AB }{2}\) = \(\frac{ 20.4 }{2}\)

= DE = 10.2 cm

FD = \(\frac{ AC }{2}\) = \(\frac{ 18.8 }{2}\)

= FD = 9.4 cm

The perimeter (in cm) of the ΔDEF

= DE + EF + FD  = 10.2 + 12.8 + 9.4 = 32.4 cm