In triangle ABC D,E and F are the midpoints of AB,BC and CA respectively. if the perimeter of triangle DEF is 30 cm then the perimeter of triangle of ABC is
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3
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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2
Answer:
you just put your formula
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