Question

The given figure shows a parallelogram ABCD. E is a point in AD and CE produced meets BA produced at point F. If AE = 4 cm, AF = 8 cm and AB = 12 cm, find the perimeter of the parallelogram ABCD.

Answer 1

AF = 8 cm and AB = 12cm

So, FB = 20 cm

In ΔDEC and ΔEAF

∠DEC = ∠EAF  ...(Vertically opposite angles)

∠EDC = ∠EAF   ...(Alternate angles)

So, ΔDEC ∼ ΔAEF  ...(AA criterion for similarity)

`=> (DE)/(AE) = (EC)/(EF) = (DC)/(AF)`

`=> (DE)/(AE) = (DC)/(AF)`

`=> (DE)/(AE) = (AB)/(AF)`

`=> (DE)/4 = 12/8`

`=>` DE = 6 cm

So, AD = AE + ED

= 4 + 6

= 10 cm

Perimeter of the parallelogram ABCD

= AB + BC + CD + AD

= 12 + 10 + 12 + 10

= 44 cm