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In △ABC, D, E and F are the midpoints of BC, CA and AB respectively. If AC=16 cm, BC=18 cm, AB=20 cm, then the perimeter of quadrilateral AEDF is .
 


Your Answer
A
32 cm
Your Answer
B
34 cm
Your Answer
C
40 cm
Correct Answer
D
36 cm

Solution

The correct option is D 36 cm
Given that,
AC=16 cm, BC=18 cm, AB=20 cm.In △ABC,
D and F are the mid-points of BC and AB,
By mid-point theorem,
DFAC
DF=12AC=12×16=8cm
AE = 12AC=162=8cm
In  quadrilateral AEDF, 
A pair of side is parallel and equal
DFAE,DF=AE=8cm
AEDF is a parallelogram
AF=12AB=12×20=10cm
AF = ED = 10 cm 
Perimeter pf parallelogram AEDF = AE + DF + AF + ED 
= (8 + 8 + 10 + 10) cm
= 36 cm
Hence, the perimeter of the parallelogram AEDF is 36 cm.

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