Question

In △ABC, D and E are points on side AB and AC respectively such that DE II BC and AD: DB = 3 : 1. If EA = 3.3 cm, then AC =

A. 1.1 cm 

B. 4 cm 

C. 4.4 cm 

D. 5.5 cm

Answer 1

From the given figure ΔABC, DE || BC. 

Let AC = x cm. 

We know that basic proportionality theorem states that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio

Then 

\(\frac{AD}{AB}\) = \(\frac{AE}{AC}\)

⇒ \(\frac{AD}{AD+BD}\) = \(\frac{3.3}{x}\)

⇒ \(\frac{AD}{AD+{\frac{1}{3}}AD}\) = \(\frac{3.3}{x}\)

⇒ x = 4.4 cm 

∴ AC = 4.4 cm