Question

38. In the given figure, ABCD is a parallelogram in which DC is extended to F such that AF intersects BC at E. Then perimeter of ABE =

(a) 35 cm (c) 40 cm (b) 36 cm (d) 45 cm​

Answer 1

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=80cm2   --- ( 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=1280

∴   AD=6.66cm

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Answer 2

Given :- In the given figure, ABCD is a parallelogram in which DC is extended to F such that AF intersects BC at E.

To Find :- perimeter of ∆ABE = ?

(a) 35 cm (c) 40 cm (b) 36 cm (d) 45 cm

Solution :-

In ∆ABE and ∆FCE we have,

→ ∠ABE = ∠FCE { since opposite sides of ll gm are parallel to each other . So, AB || DC and BC is a transversal . Then, alternate interior angles are equal in measure . }

→ ∠AEB = ∠FEC { Vertically opposite angles }

So,

→ ∆ABE ~ ∆FCE { By AA similarity. }

then,

→ AB/FC = BE/CE = AE/FE { when two ∆'s are similar their corresponding sides are in same ratio .}

therefore,

→ 15/6 = BE/4 = AE/8

→ 5/2 = BE/4

→ 2•BE = 20

→ BE = 10 cm .

and,

→ 15/6 = AE/8

→ 5/2 = AE/8

→ 2•AE = 40

→ AE = 20 cm

hence,

→ Perimeter ∆ABE = AB + BE + AE

→ Perimeter ∆ABE = 15 + 10 + 20

→ Perimeter ∆ABE = 45 cm (Ans.)

∴ perimeter of ∆ABE is equal to 45 cm .

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