Question

In a triangle ABC, D, E, F are the midpoints of AB, BC, AC respectively.
DF = 5cm , EF = 9 cm, DE = 6 cm then perimeter of the Δ ABC IS?


Please with explanation and diagram


CLASS 10

Answer 1

Step-by-step explanation:

It is given that , In Δ AB C , D, E and F are mid points of AB, BC and CA respectively.

Also, AB=6 cm, BC= 7.2 cm, and CA= 7.8 cm

Keep in mind :

Line segment joining the mid point of two sides of triangle is parallel to third side and is half of it.

So, DE ║AC,and DE=  

EF║AB, and FE=  

DF║BC ,and D F=  

DF=  cm,

DE= cm,

EF= cm,

So, Perimeter of Δ ABC=AB +BC+CA

             =  6  + 7.8 +7.2

              = 21 cm

Perimeter of ΔDEF=DE +E F +D F

          =3 +3.6 +3.9

       = 6.6 +3.9

       = 10.5 cm