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.

 

Answer 1

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