Question

In a Triangle ABC, D, E, F are respectively, the midpoints of BC,CA and AB. If the lengths of sides AB, BC and CA are 17cm , 28 cm and 19 cm. find the perimeter of Triangle DEF.​

Answer 1

Answer:

Question:- Find perimeter of ∆DEF

Given:-

D,E,F are the midpoints of BC,CA and AB respectively

AB=17 cm

BC=28 cm

CA=19 cm

Solution:-

F is the midpoint of AB

thus

AF+BF=AB=17 cm

AF=BF=17/2=8.5

also

D is the midpoint of BC

then

BD+DC=BD=28

BC=BD=14

In ∆FBD

FB=8.5 BD=14 DF=?

also

E is the midpoint of AC

that is

AE+EC=AC=19

AE=EC=19/2=9.5

also DC=14 (already found)

In ∆DEC

DC=14 CE=9.5 DE=?

Also

FA=8.5 EA=9.5 EF=?

We've to take the half of all given angles for finding the answer

that is

9.5+8.5+14

=18+14

=32

therefore the perimeter of ∆DEF is 32cm

Hope it helps