Question

In the given figure, DE $\parallel$ CB. Determine AC and AE.

Answer 1

Given In $△ACB,DE\parallel CB$

$\therefore \angle ADC=\angle ACB$ and $\angle AED=\angle ABC$

$△ADE\sim △ACB$ (by AAA similarity )

$\therefore \frac{AD}{AC}=\frac{DE}{CB}$

$⟹\frac{14}{AC}=\frac{12}{15}$

$\therefore AC=17.5$ cm

Similarly, $\frac{AE}{AB}=\frac{DE}{CB}$

$\frac{AE}{4}=\frac{12}{15}$

$\therefore AE=3.2$ cm