In a ΔABC, D, E and F are the mid-points of side BC, CA and AB respectively. If BC = 14.4 cm, CA = 15.2 cm and AB = 12.4 cm, what is the perimeter (in cm) of the ΔDEF ?
Answer & explanation
Correct answer: option 3
F and E are the mid point of AB and AC
So, according to the concept,
FE = (\(\frac{BC}{2}\))
Similarly,
DE = (\(\frac{AB}{2}\)) and FD = (\(\frac{AC}{2}\))
Now,
Perimeter of ΔDEF = DE + FE + FD
⇒ (\(\frac{BC}{2}\)) + (\(\frac{AB}{2}\)) + (\(\frac{AC}{2}\))
⇒ (\(\frac{1}{2}\))(BC + AB + AC)
⇒ (\(\frac{1}{2}\))(14.4 + 12.4 + 15.2)
⇒ (\(\frac{1}{2}\))(42)
⇒ 21
Therefore, the perimeter of ΔDEF is 21.