Question

In a triangle ABC, angle ABC = 90 and BD is perpendicular to AC. If BD = 8 cm and AD = 4 cm then find the length of CD?

Answer 1

`CD=16` cm

Explanation:

Given `angleABC=90^@, BD` is perpendicular to `AC`, `BD=8, and AD=4`, as shown in the diagram.
Let `angleACB=x, =>angleCBD=90-x`
`=> angleABD=x, =>angleBAD=90-x`
`=> DeltaABC, DeltaADB, and DeltaBDC` are similar

`=> (BD)/(CD)=(AD)/(DB)`
`=> 8/(CD)=4/8`
`=> CD=(8xx8)/4=16`