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Question
In the given figure, A – D – C and B – E – C seg DE || side AB If AD = 5, DC = 3, BC = 6.4 then Find BE.
Solution
Let BE be x.
BE + CE = BC ...(∵ B - E - C)
∴ x + CE = 6.4
∴ CE = (6.4 − x)
In Δ ABC,
seg DE || side AB ...(Given)
∴ By basic proportionality theorem,
`("CD")/("DA") = ("CE")/("BE")`
∴ `3/5 = (6.4 - "x")/"x"`
∴ 3x = 5(6.4 − x)
∴ 3x = 32 − 5x
∴ 3x + 5x = 32
∴ 8x = 32
∴ x = `32/8`
∴ x = 4
BE = x = 4
∴ BE = 4
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