Question

In the following figure, point $D$ divides $AB$ in the ratio $3:5$. Find:

iv) $DE=2.4cm$, find the length of $BC$.

Answer 1

Step : Finding the length of $BC$.

Given: $AD:DB=3:5,DE=2.4cm$



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

$\angle ADE=\angle ABC$ [Corresponding angles]

$\angle AED=\angle ACB$ [Corresponding angles]

By $AA$ criterion, $\Delta ADE\sim \Delta ABC$

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

$\Rightarrow \frac{3}{8}=\frac{2.4}{BC}$ [$\frac{AD}{AB}=\frac{3}{8}$, from part (ii)]

$\Rightarrow BC=6.4cm$

Hence, the length of $BC$ is $6.4cm$.