Question

33. In the below diagram, the perimeter of triangle ABC is 27 cm. If D is the mid-point of AB and
DE || BC, then find the length of DE.​

Answer 1

Answer:

5cm

Step-by-step explanation:

D is midpoint of ab

therefore ad = BD

bd = 4.5cm

ab = 9cm

and by converse of midpoint theorem e is also midpoint of AC

therefore ae = CE

CE = 4cm

AC = 8cm

and perimeter = 27cm ( a+b+c )

AB + BC + AC = 27cm

9cm+BC+8cm = 27cm

BC = 10cm

it is given that

DE || BC and D is the midpoint of AB

therefore DE = 1/2BC. (( midpoint theorem ))

DE = 1/2*10

DE = 5cm