Question

In the given figure $\Delta ABC$ and $\Delta DEF$ are shown with the given side lengths. If $AL$ and $DM$ are the perpendicular frorm the vertex $A$ and $D$ respectively, Find $\frac{DM}{AL}$.

Answer 1

$\Rightarrow$ $\frac{AB}{DE}=\frac{5}{10}=\frac{1}{2}$

$\Rightarrow$ $\frac{BC}{EF}=\frac{4}{8}=\frac{1}{2}$

$\Rightarrow$ $\frac{AC}{DF}=\frac{4.2}{8.4}=\frac{1}{2}$

$\therefore$ $\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}=\frac{1}{2}$

$\therefore$ $△ABC\sim △DEF$

Now, use the result that in similar triangles the ratio of corresponding altitudes is the same as the ratio of corresponding sides.

$\therefore$ $\frac{AL}{DM}=\frac{1}{2}$