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Question

# 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 .

A
32 cm
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B
34 cm
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C
40 cm
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D
36 cm
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Solution

## The correct option is D 36 cmGiven 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, DF∥AC DF=12AC=12×16=8cm AE = 12AC=162=8cm In quadrilateral AEDF, A pair of side is parallel and equal DF∥AE,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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