Question

In figure, AB, CD, EF are the ⊥rs to BF. Find CD if AB = 12 cm and EF = 10 cm.

Answer 1

The value of CD is 5.45 cm.

In ∆ABF and ∆CDF

ang(ABF)=Ang(CDF)= 90°

Ang(CFB) ( common)

So,

∆ABF ~ ∆CDF( by AA similarty)

Similarly, ∆ CBF~∆CBD

AB/CD= BF/DF and EF/CD= BF/BD

equating BF

AB×DF=EF×BD

AB/EF = BD/DF

12/10=BD/DF=6/5

AB/CD=BF/DF

12/CD= (BD+DF)/DF

12/CD=BD/DF +1

12/CD= 6/5+1

12/CD=11/5

CD=60/11 cm

CD = 5.45 cm