Question

in the given figure ABCD is a parallelogram AE perpendicular to DC and CF perpendicular to AD. If AB =16cm, AE =8cm, CF=10cm .Find AD Explain

Answer 1

we know that to find area of parallelogram the formula is base X height
now, AE ×DC = 16×8
AD ×CF = AD ×10
BECAUSE THE AREA WILL BE THE SAME
EQUATING BOTH
AE × DC = AD× CF
16×8 = AD× 10
AD = 16×8/10
AD = 128/10
AD = 12.8 CM
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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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