Question

In the figure given above, if DE $\parallel$ BC, then the value of x equals to:

• A. 3 cm
• B. 2 cm
• C. 4 cm
• D. 6.7 cm

Answer 1

The correct option is D 6.7 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 rule

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

$\therefore \frac{3}{2+3}=\frac{4}{x}\Rightarrow x=6.7cm$