Question

In the given figure, $DE\parallel BC$. If $\frac{AD}{DB}=\frac{3}{5}$ and $AC=5.6cm$, find $AE$.

• A. $5.1cm$
• B. $3.9cm$
• C. $2.1cm$
• D. None of these
  

Answer 1

The correct option is C $2.1cm$

Given: $\frac{AD}{DB}=\frac{3}{5}$ and $AC=5.6cm$ and $DE\parallel BC$
Since, $DE\parallel BC$, by Equal Intercept Theorem,
$\frac{AD}{BD}=\frac{AE}{EC}$
$\frac{AE}{EC}=\frac{3}{5}$
Let $AE=3x$ , $EC=5x$
$AE+EC=AC$
$3x+5x=5.6$
$8x=5.6$
$x=0.7$
Hence, $AE=3\times 0.7$
$AE=2.1$cm