In a ΔABC, D, E and F are mid-points of sides AB, AC and BC respectively. If DE and DF are joined, find the perimeter of BDEF.
Answers
Answer:
Given in △ABC, D,E,F are the mid points of sides AB,BC and CA respectively
Now using mid point theorem line segment joining the mid points of two sides is parallel to third side and also half of it.
∴DF=
2
1
BC
⇒
BC
DF
=
2
1
.......(i)
Similarly
AC
DE
=
2
1
.........(ii)
AB
EF
=
2
1
...........(iii)
Using (i),(ii) and (iii)
BC
DF
=
AC
DE
AB
EF
=
2
1
BC
DF
=
AC
DE
AB
EF
=
2
1
∴△ABC∼△DEF
Now if triangles are similar then ratio of their perimeter is equal to ratio of of their corresponding sides.
Perimeeter(△ABC)
Perimeter(△DEF)
=
2
1
⇒ Perimeter of △ABC=
2
1
×12.8=6.4 cm
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Answer:
= 7 cm, BC = 8 cm, AC = 9 cm
In ∆ABC,
F and E are the mid points of AB and AC.
∴ EF = 1/2 BC
Similarly
DF = 1/2 AC and DE = 1/2 AB
Perimeter of ∆DEF = DE + EF + DF
= (1/2) AB + (1/2) BC + (1/2) AC
= 1/2 ∗7 + 1/2 ∗8 + 1/2 ∗9
= 3.5 + 4 + 4.5
= 1/2 cm
Perimeter of ΔDEF = 1/2 cm
Step-by-step explanation: