Question

In the given figure, DE || BC and `(AD)/(DB) = 2/5`. If AC = 5.6 cm, then EC is equal to ______.

पर्याय

• 1.4 cm

• 2.8 cm

• 3.6 cm

• 4 cm

Answer 1

In the given figure, DE || BC and `(AD)/(DB) = 2/5`. If AC = 5.6 cm, then EC is equal to 4 cm.

Explanation:

Since DE || BC, by the Basic Proportionality Theorem (Thales theorem):

`(AD)/(DB) = (AE)/(EC)`

Given,

`(AD)/(DB) = 2/5` ⇒ `(AE)/(EC) = 2/5`

So, let AE = 2x and EC = 5x

Then,

AC = AE + EC

AC = 2x + 5x

AC = 7x

Given AC = 5.6,

7x = 5.6

x = `5.6/7`

∴ x = 0.8

EC = 5x

= 5 × 0.8

∴ EC = 4 cm