Question

Please solve this?

puza academy

Answer 1

C) `5`

Explanation:

Given `AB=AC, and angleADB=90^@`
`=> BD=DC`
`DeltaCHE, DeltaCAD, DeltaBAD and DeltaBFE` are all similar,
`=> (CE)/(HE)=(BE)/(FE), => (CE)/2=(BE)/8, => BE=4CE`,

Let `CE=a, => BE=4a, => BC=BE+EC=5a`,
`=> BD=DC=(BC)/2=(5a)/2`
`=> x/(BD)=(FE)/(BE)`
`=> x=BD*(FE)/(BE)=(5a)/2*8/(4a)=5`

Footnotes : `DeltaBAD and DeltaCAD` are actually congruent. :)