In a ∆ABC, D, E and F are the mid-points of side BC, CA and AB respectively. If BC = 25.6cm, CA = 18.8cm and AB = 20.4cm, what is the perimeter (in cm) of the ∆DEF?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 32.4
Given:
∆ABC, D, E and F are the mid-points of side BC, CA and AB
BC = 25.6cm, CA = 18.8cm and AB = 20.4cm
Understanding:
Mid point theorem states that 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
Calculations:
D, E and F are the mid points of BC, AC and AB.
By using mid point theorem, we get
AF/FB = AE/EC and EF = BC/2
EF = 25.6/2 = 12.8 cm
Similarly, DE = AB/2 = 10.2 and DF = AC/2 = 9.4
Thus, the perimeter of triangle DEF
= DF + DE + EF = 12.8 + 9.4 + 10.2 = 32.4 cm