Question

in a triangle abc,d,e and f are respectively,the mid-point of bc,ca and ab.if the lengths of sides ab,bc,ca are 17cm,18cm and 19cm,respectively,find the perimeter of triangleDEF

Answer 1

perimeter of triangle DEF,
= 8.5+9.5+9
= 27 cm

Answer 2

Answer: The perimeter of Δ DEF is 27 cm

Step-by-step explanation:

As given in question ABC is a triangle and D, E, F are the mid points of side AB,BC, AC resp.

BC= 18cm , AB=17cm, AC= 19cm

Now as we know by Mid point theorem: In a triangle the line that join the mid points two sides of a triangle is parallel to the third side moreover it is half of the third side.

Therefore by mid point theorem

FE║ BC and FE= $\dfrac{1}{2} \times BC= \dfrac{1}{2} \times 18= 9cm$

ED║AB and ED =  $\dfrac{1}{2} \times AB= \dfrac{1}{2} \times 17= 8.5cm$

DF║ AC and DF =$\dfrac{1}{2} \times AC= \dfrac{1}{2} \times 19= 9.5cm$

Therefore perimeter of Δ DEF = ED+ FE+ DF= 8.5+9+9.5= 27 cm

Hence, the perimeter of Δ DEF is 27 cm