Question

ABCD is a parallelogram .AE is perpendicular to DC and CD is perpendicular to AD .if AB=cms AE=8cms and CF=16 Cms then show that AD=6cms

Answer 1

Draw the diagonal AC. Now your parallelogram will be devided to two traingles with equal AREA. 
Lets take Traingle: ADC. 
FC is the perpendicular to AD(Base). so Area will be: 1/2 x AD x CF 

AE is the perpendicular to DC so Area will be : 
1/2 x DC x AE=1/2 x AB x AE, for parallelogram DC=AB. 

Hence, 1/2 x AD x CF =1/2 x AB x AE 
=> AD= AB x AE/CF= 16 x 8/10=128/10=12.8cm 

Answer: 12.8cm

(*****NOTE==U have a mistake in ur question,it should be ABCD is a parallelogram, AE perpendicular to DC & CF perpendicular to AD.If AB=16cm,AE=8cm &CF=10cm,find AD*****)

Answer 2

Question :-

In figure, ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD.

Answer :-

We have, AE ⊥ DC and AB = 16 cm

∵ AB = CD [Opposite sides of parallelogram]

∴ CD = 16 cm

Now, area of parallelogram ABCD = CD x AE

= (16 x 8) cm2 = 128 cm2 [∵ AE = 8 cm]

Since, CF ⊥ AD

∴ Area of parallelogram ABCD = AD x CF

⇒ AD x CF = 128 cm

⇒ AD x 10 cm = 128 cm2 [∵ CF= 10 cm]

⇒ AD = 128/10 cm = 12.8 cm 10

Thus, the required length of AD is 12.8 cm

Hope it helps ❤ Mrk as brainliest