In the adjoining figure, AD = BD and DE || BC. If AC = 6 cm and DE = 4 cm, then the length of BC is :

1. 4 cm

2. 5 cm

3. 6 cm

4. 8 cm

Given,

D is the mid-point of AB.

By converse of mid-point theorem,

A line drawn through the midpoint of one side of a triangle, and parallel to another side, will bisect the third side.

In △ABC,

Since, D is the mid-point of AB and DE // BC, thus :

E is 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 || BC

⇒ DE = $\dfrac{1}{2}$ BC

⇒ BC = 2 DE

⇒ BC = 2 × 4

⇒ BC = 8 cm.

Hence, option 4 is the correct option.