Question

In the given figure, AE : EC = 2 : 3 and BC = 20 cm then DE is equal to ______.

Options

• 10 cm

• 12 cm

• 8 cm

• 16 cm

Answer 1

In the given figure, AE : EC = 2 : 3 and BC = 20 cm then DE is equal to 8 cm. 

Explanation: 

From figure,

In △ ADE and △ ABC,

⇒ ∠DAE = ∠BAC (Common angle)

⇒ ∠ADE = ∠ABC (Corresponding angles are equal)

∴ △ ADE ~ △ ABC (By A.A. postulate)

Given,

AE : EC = 2 : 3

Let AE = 2x and EC = 3x

From figure,

AC = AE + EC = 2x + 3x = 5x

We know that,

Corresponding sides of similar triangle are in proportion.

∴ `(DE)/(BC) = (AE)/(AC)`

⇒ `(DE)/(20) = (2x)/(5x)`

⇒ DE = `20 × 2/5`

⇒ DE = `40/5`= 8 cm