Question

In the given figure, DE || BC. If AD = 6 cm, AB = 24 cm and DE = 5 cm, then find the value of BC.

Answer 1

Consider $△ADE$ and $△ABC$,

Given, DE || BC

$\angle$ ADE = $\angle$ ABC
$\angle$ AED =$\angle$ ACB
(Since corresponding angles are equal)

$\therefore △ADE\sim △ABC$ (by AA similarity criterion)

$\Rightarrow \frac{DE}{BC}=\frac{AD}{AB}$
(corresponding sides of similar triangles are in same ratio)

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

$\Rightarrow BC=\frac{5\times 24}{6}$

$\Rightarrow BC=20cm$