Question

In figure ⬆

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

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Answer 1

Answer:-

BSOWe 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 =$\frac{128}{10}$

Thus, the required length of AD is 12.8 cm

hope it helps u...!!

Answer 2

Given,

Given,AB=10cm, AE=8cm, and CF=12cm.

AB=DC=10cm --------(1)

AB=DC=10cm --------(1)[Opposite sides of parallelogram are equal]

AB=DC=10cm --------(1)[Opposite sides of parallelogram are equal]Area of parallelogram ABCD=b×h

AB=DC=10cm --------(1)[Opposite sides of parallelogram are equal]Area of parallelogram ABCD=b×h =DC×AE

AB=DC=10cm --------(1)[Opposite sides of parallelogram are equal]Area of parallelogram ABCD=b×h =DC×AE = 10×8

AB=DC=10cm --------(1)[Opposite sides of parallelogram are equal]Area of parallelogram ABCD=b×h =DC×AE = 10×8Area of parallelogram ABCD=80cm² -------(2)

AB=DC=10cm --------(1)[Opposite sides of parallelogram are equal]Area of parallelogram ABCD=b×h =DC×AE = 10×8Area of parallelogram ABCD=80cm² -------(2)And also,

AB=DC=10cm --------(1)[Opposite sides of parallelogram are equal]Area of parallelogram ABCD=b×h =DC×AE = 10×8Area of parallelogram ABCD=80cm² -------(2)And also,Area of parallelogram ABCD=CF×AD

AB=DC=10cm --------(1)[Opposite sides of parallelogram are equal]Area of parallelogram ABCD=b×h =DC×AE = 10×8Area of parallelogram ABCD=80cm² -------(2)And also,Area of parallelogram ABCD=CF×AD 80=12×AD [From (2)]

AB=DC=10cm --------(1)[Opposite sides of parallelogram are equal]Area of parallelogram ABCD=b×h =DC×AE = 10×8Area of parallelogram ABCD=80cm² -------(2)And also,Area of parallelogram ABCD=CF×AD 80=12×AD [From (2)]$ad \: = \frac{80}{12}$

AB=DC=10cm --------(1)[Opposite sides of parallelogram are equal]Area of parallelogram ABCD=b×h =DC×AE = 10×8Area of parallelogram ABCD=80cm² -------(2)And also,Area of parallelogram ABCD=CF×AD 80=12×AD [From (2)]$ad \: = \frac{80}{12}$AD=6.66cm