Question

ABCD is a parallelogram, AE is perpendicular to DC and CF is perpendicular to AD. If AB=16 cm, AE=8 cm and CF=10 cm, find AD.

Answer 1

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Given,

• AB = CD = 16 cm (Opposite sides of a parallelogram)
• CF = 10 cm and AE = 8 cm

Now,

$\bullet{\underline{\boxed{\sf\pink{Area\:of\:parallelogram = Base \times Altitude}}}}$

⇒ CD × AE = AD × CF

⇒ 16×8 = AD × 10

⇒ AD = 128/10 cm

⇒ AD = 12.8 cm

Therefore,

AD is equal to 12.8 cm.

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

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