Question

In the given figure, find the value of $AE$ if $AC=5.6$ cm and $DE||BC$.

• A. 2.4 cm
• B. 2.1 cm
• C. 2.2 cm
• D. 2.5 cm

Answer 1

The correct option is B 2.1 cm

In given figure $\angle ADE=\angle ACB$ and $AC=5.6$ cm

$DE\parallel BC$

$\angle BAC=\angle DAE$ ...... (Common angle)

Then $\angle ABC=\angle AED$

$\therefore \Delta ADE\sim \Delta ABC$ ...... [By AAA postulates of similarity]

$\therefore \frac{AD}{AB}=\frac{AE}{AC}$

$\Rightarrow \frac{3}{3+5}=\frac{AE}{5.6}$

$\Rightarrow AE=\frac{3}{8}\times 5.6=2.1$ cm