Question

In the given figure, $DE//BC$, $AE$ = $15$ cm, $EC$ = $9$ cm, $NC$ = $6$ cm and $BN$ = $24$ cm.Find lengths of $ME\left(incm\right)$.

Answer 1

Given: $DE\parallel BC$,
In $△ADM$ and $△ABN$,
$\angle DAM=\angle BAN$ (Common angle)
$\angle ADM=\angle ABN$ (Corresponding angles)
$\angle AMD=\angle ANB$ (Corresponding angles)
Thus, $△ADM\sim △ABN$ (AAA rule)
Similarly, $△AME\sim △ANC$ and $△ADE\sim △ABC$
Since, $△AME\sim △ANC$
$\frac{AE}{AC}=\frac{ME}{NC}$ (Corresponding sides)

$\frac{15}{24}=\frac{ME}{6}$

$ME=\frac{15\times 6}{24}$

$ME=3.75$ cm