Question

In the above figure, if DE || BC, then x equals :

• A. 6 cm
• B. 7 cm
• C. 3 cm
• D. 4 cm

Answer 1

The correct option is A 6 cm

In $△ADE$ and $△ABC$

$\angle ADE=\angle ABC$ (As $DE\parallel BC$ Corresponding angles)

$\angle AED=\angle ACB$ (As $DE\parallel BC$ Corresponding angles)

$\angle DAE=\angle BAC$ (common angle)

$\therefore △ADE\sim △ABC$ by AAA similarity.
If two triangles are similar, then their corresponding sides are proportional.

$\Rightarrow \frac{AD}{AB}=\frac{DE}{BC}\frac{3}{7}=\frac{x}{14}x=\frac{3\times 14}{7}\Rightarrow x=6$