Question

In the given figure, $\Delta ABC\sim \Delta ADE$. If
$AE:EC=4:7$ and $DE=6.6cm,$ find $BC$. If x be the length of the perpendicular from $A$ to $DE$, find the length of perpendicular from $A$ and $BC$ in terms of $x.$

Answer 1

Given $\frac{AE}{EC}=\frac{4}{7}$

$\frac{EC}{AE}=\frac{7}{4}$

$\frac{EC+AE}{AE}=\frac{7+4}{4}$

$\frac{AC}{AE}=\frac{11}{4}$
Given, $△ABC\sim △ADE$
$\frac{AC}{AE}=\frac{BC}{DE}$

$\frac{11}{4}=\frac{BC}{6.6}$

$\therefore BC=18.15$ cm
The perpendiculars of similar triangles are in proportion to their sides, Hence, perpendicular from A on BC = $\frac{AC}{AE}$ (perpendicular from A on DE)
Perpendicular from A on BC = $\frac{11}{4}x$