BD is the median of triangle ABC. F is a point on AB such that CF intersects BD at E and BE=ED. If BF =5cm. Then BA=?
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Answer:
AB=3 and FB=3×5=15 units
Step-by-step explanation:
Let |ABC| denote area of ABC
let |ABC|=12a,
as AD=DC,⇒|BDC|=|BDA|=12a2=6a
as BE=ED,⇒|BEC|=|DEC|=6a2=3a,
let |BFE|=x,⇒|DFE|=x,
⇒|AFD|=|BDA|−|BDF|=6a−2x
As AD=DC,⇒|AFD|=|CFD|,
⇒6a−2x=3a+x
⇒x=a
⇒|CFB|=3a+x=4a
=> AB:FB=>|ABC|:|CFB|=12a:4a=3:1
=>AB=3 and FB=3×5=15 units
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