Question

In given figure, If $\angle ADE=\angle B$ show that $△ADE\sim △ABC$. If $AD=3.8cm,AE=3.6cm,BE=2.1cm$ and $BC=4.2cm$, find $DE$.

Answer 1

In $\Delta ADE$ and $\Delta ABC$,

$\angle ADE=\angle B$ and $\angle A=\angle A$

So, by AA criteria, $\Delta ADE\sim \Delta ABC$, then,

$\Rightarrow$ $\frac{AD}{AB}=\frac{DE}{BC}$

$\Rightarrow$ $\frac{AD}{AE+EB}=\frac{DE}{BC}$

$\Rightarrow$ $\frac{3.8}{3.6+2.1}=\frac{DE}{4.2}$

$\Rightarrow$ $DE=2.8cm$