D, E and F are respectively the mid-points of the sides BC, CA and AB of a ABC. If BC = 10 cm, CA = 12 cm and AB = 17 cm, then the perimeter of the DEF is :

1. 13 cm

2. 19.5 cm

3. 39 cm

4. None of these

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

⇒ FE || BC and FE = $\dfrac{1}{2} BC = \dfrac{1}{2}$ × 10 = 5 cm

Since, F and D are the mid-points of AB and BC respectively.

⇒ FD || AC and FD = $\dfrac{1}{2} AC = \dfrac{1}{2}$ × 12 = 6 cm

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

⇒ DE || AB and DE = $\dfrac{1}{2}AB = \dfrac{1}{2}$ × 17 = 8.5 cm

Perimeter of DEF = DE + FE + FD = 8.5 + 5 + 6 = 19.5 cm

Hence, option 2 is the correct option.