Question

In the given figure, if $AD=4cm,CD=12cmandar\left(\Delta ADB\right)=kar\left(\Delta BDC\right),$ then k equals

• A.
  12
• B.
  3
• C.
  $\frac{1}{3}$
  
• D.
  $\frac{1}{4}$
  

Answer 1

The correct option is C

$\frac{1}{3}$

Given:
$AD=4cm,CD=12cmandAr\left(\Delta ADB\right)=kAr\left(\Delta BDC\right)LetBE\perp AC.Since,Ar\left(\Delta ADB\right)=kAr\left(\Delta BDC\right)\therefore \frac{1}{2}\times AD\times BE=k\times \frac{1}{2}\times CD\times BE\Rightarrow AD=k\times CD\Rightarrow 4=k\times 12\Rightarrow k=\frac{1}{3}$

Hence, the correct answer is option (c).