D
5. In the given figure, ABCD is a parallelogram. CE and AF are
perpendiculars on diagonal BD. Show that
F
(1 ) AF = CE
(2) DE = BF
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2
Answer:
In parallelogram ABCD, we have given AB=10cm, AE=8cm, and CF=12cm.
⇒ AB=DC=10cm [Opposite sides of parallelogram are equal]
⇒ Lets find out area of parallelogram with height AE and base DC.
⇒ Area of parallelogram ABCD=b×h
⇒ Area of parallelogram ABCD=DC×AE
⇒ 10×8
∴ Area of parallelogram ABCD=80cm
2
--- ( 1 )
⇒ Now, to find area of parallelogram let CF be the height and AD will be base.
⇒ Area of parallelogram ABCD=CF×AD
⇒ 80=12×AD [From ( 1 )]
⇒ AD=
12
80
∴ AD=6.66cm
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