On the sides AB and AC of a △ABC, D and E are two points such that AD : AB = AE : AC = 1 : 2. If BC = 7 cm, then DE =

1. 3.5 cm

2. 7 cm

3. 14 cm

4. 15 cm

Given,

AD : AB = 1 : 2

⇒ AB = 2 AD

∴ D is the mid-point of AB

AE : AC = 1 : 2

⇒ AC = 2 AE

∴ E is the mid-point of AC

By mid-point theorem,

The line segment joining the mid points of any two sides of a triangle is parallel to the third side and is equal to half of it.

Since, D and E are the mid-points of AB and AC respectively.

⇒ DE = $\dfrac{1}{2} BC = \dfrac{1}{2}$ × 7 = 3.5 cm

Hence, option 1 is the correct option.