Question

If ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 10 cm, AE = 6 cm and CF =

5 cm, then AD is equal to:

A. 10cm

B. 6cm

C. 12cm

D. 15cm​

Answer 1

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

Answer 2

Solution :-

In ll gm ABCD given that,

→ AB = 10 cm

→ AE ⊥ DC

→ CF ⊥ AD

→ AE = 6 cm .

→ CF = 5 cm .

So,

→ DC = AB { Opposite sides of ll gm are equal }

→ DC = 10 cm .

then,

→ Area of ll gm = Base * Height

→ Area of ll gm = DC * AE

→ Area of ll gm = 10 * 6

→ Area of ll gm = 60 cm² .

also,

→ Area of ll gm = AD * CF

→ 60 = AD * 5

→ AD = 60/5

→ AD = 12 cm (Ans.) (C)

Hence, AD is equal to 12 cm .

Learn more :-

In the figure along side, BP and CP are the angular bisectors of the exterior angles BCD and CBE of triangle ABC. Prove ∠BOC = 90° - (1/2)∠A .

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