Question

In the adjacent figure, ABCD is a parallelogram, CE AB produced and BF AD
(a) If AD = 10cm, CE = 8cm, and BF = 12cm, find AB.
(b) If AB = 16cm, AD = 12cm and CE = 10cm, find BF. ​

Answer 1

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MATHS

In the figure, ABCD is a parallelogram. If DE = 4 cm, then BF equals :

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ANSWER

⇒ In given figure ABCD is a parallelogram.

⇒ AB=DC=6cm and AD=BC=3cm ---(1) [Opposite sides of parallelogram are parallel and equal]

⇒ We can see in figure DE ⊥ AB

⇒ So, area of parallelogram ABCD with height DE and baseAB is,

⇒ Area of parallelogram ABCD =

2

1

×AB×DE

⇒

2

1

×6×4 [From ( 1 )]

∴ Area of parallelogram ABCD=12cm

2

----- ( 2 )

⇒ In figure BF⊥AD

⇒ So now we can take BF as a height and AD as a base.

⇒ Area of parallelogram ABCD=

2

1

×AD×BF

⇒ 12=

2

1

×3×BF [From ( 1 ) and ( 2 )]

⇒ BF=

3

24

∴ BF=8cm

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