Question

10. The given figure shows a parallelogram ABCD.
E is a point in AD and CE produced meets
BA produced at point F. If AE = 4 cm,
AF = 8 cm and AB = 12 cm, find the
perimeter of the parallelogram ABCD.
D
С
E
F
A
B​

Answer 1

Step-by-step explanation:

In

△

AFEand △BFC,

∠AFE=∠BFC (Common angle)

∠AEF=∠BCF (Corresponding angles of parallel lines)

∠FAE=∠CBF (Corresponding angles of parallel lines)

Thus,

△AFE∼△CFB(AAA rule)

Hence, AFBF=AEBC

AFAF+AB=AEBC

88+12=4BC

BC=4×208

BC=10 cm

Perimeter of parallelogram = AB+BC+BC+AD

Perimeter of parallelogram = 2(AB+BC)

Perimeter of parallelogram = 2(12+10) (Opposite sides are equal)

Perimeter of parallelogram = 44cm

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