Question

In the given figure; if $\text{DE}\parallel \text{BC}\frac{\text{DE}}{\text{BC}},$ then calculate x.

Answer 1

In the given figure; if $DE\parallel BC\frac{DE}{BC}$ then calculate $x$

In $△ADE$ & $△ABC$

$\angle A$ is common

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

$\therefore △ADE\sim △ABC$ ($A-A$ Test)

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

$\frac{DE}{BC}=\frac{AD}{AD+DB}$

$\frac{x}{14}=\frac{3}{3+4}$

$\frac{x}{14}=\frac{3}{7}$

$x=\frac{42}{7}$

$x=6$