Question

In $\Delta ABC$, DE is || to BC, meeting AB and AC at D and E. If AD = 3 cm, DB = 2 cm and AE = 2.7 cm, then AC is equal to:

• A. $6.5$ cm
• B. $4.5$ cm
• C. $3.5$ cm
• D. $5.5$ cm

Answer 1

The correct option is B $4.5$ cm

In $△$$ADE$ and $△$$ABC$,

$\angle$$ADE=$$\angle$$ABC$ (corresponding angles)

$\angle$$AED=$$\angle$$ACB$ (corresponding angles)

so,$△$$ADE$ $\sim$$△$$ABC$

so, $\frac{AD}{AB}=\frac{AE}{AC}$

$AC=2.7$$\times$$\frac{5}{3}$$=$$4.5$ cm