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
• B. 34 cm
• C. 40 cm
• D. 36 cm

Answer 1

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,
$DF\parallel AC$
$DF=\frac{1}{2}AC=\frac{1}{2}\times 16=8cm$
AE = $\frac{1}{2}AC=\frac{16}{2}=8cm$
In quadrilateral AEDF,
A pair of side is parallel and equal
$DF\parallel AE,DF=AE=8cm$
$\therefore$ AEDF is a parallelogram
$\Rightarrow AF=\frac{1}{2}AB=\frac{1}{2}\times 20=10cm$
AF = ED = 10 cm
$\therefore$ 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.