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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.
Solution
AF = 8 cm and AB = 12cm
So, FB = 20 cm
In ΔDEC and ΔEAF
∠DEC = ∠EAF ...(Vertically opposite angles)
∠EDC = ∠EAF ...(Alternate angles)
So, ΔDEC ∼ ΔAEF ...(AA criterion for similarity)
`=> (DE)/(AE) = (EC)/(EF) = (DC)/(AF)`
`=> (DE)/(AE) = (DC)/(AF)`
`=> (DE)/(AE) = (AB)/(AF)`
`=> (DE)/4 = 12/8`
`=>` DE = 6 cm
So, AD = AE + ED
= 4 + 6
= 10 cm
Perimeter of the parallelogram ABCD
= AB + BC + CD + AD
= 12 + 10 + 12 + 10
= 44 cm
Notes
Δ
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