d, e, f are the midpoints of sides AB, BC, CA of triangle ABC if perimeter of triangle ABC is 24 cm find the perimeter of triangle DEF
Answers
Answered by
0
Answer:
yes
Step-by-step explanation:
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Answered by
4
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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