The ABC, DE. Fare, respectively the mid-points of BC, CA and AB. If th

1.	The ABC, DE. Fare, respectively the mid-points of BC, CA and AB. If the lengths of sides AB, BC and CA are 17 om 18 cm and 19 or respectively, find the perimeter of A DEFin the figure ABCD is a paralelogram in which Aufne if the
Answer» ong>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

The ABC, DE. Fare, respectively the mid-points of BC, CA and AB. If the lengths of sides AB, BC and CA are 17 om 18 cm and 19 or respectively, find the perimeter of A DEFin the figure ABCD is a paralelogram in which Aufne if the

Answer»

ong>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=

⇒

.......(i)

Similarly

.........(ii)

...........(iii)

Using (i),(ii) and (iii)

∴△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)

⇒ Perimeter of △ABC=

×12.8=6.4 cm