Question

# 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.

A
42 cm
B
44 cm
C
46 cm
D
48 cm
E
40 cm
F
38 cm
G
36 cm

Solution

## The correct option is B $$44$$ cmIn $$\triangle AFE$$ and $$\triangle BFC$$,$$\angle AFE = \angle BFC$$ (Common angle)$$\angle AEF = \angle BCF$$ (Corresponding angles of parallel lines)$$\angle FAE = \angle CBF$$ (Corresponding angles of parallel lines)Thus, $$\triangle AFE \sim \triangle CFB$$ ($$AAA$$ rule)Hence, $$\dfrac{AF}{BF} = \dfrac{AE}{BC}$$$$\dfrac{AF}{AF + AB} = \dfrac{AE}{BC}$$$$\dfrac{8}{8 + 12} = \dfrac{4}{BC}$$$$BC = \dfrac{4 \times 20}{8}$$$$BC = 10$$ cmPerimeter 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 = $$44$$ cmMathematics

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