D, E and F are respectively the mid-points of the sides BC, CA and AB of a ABC. If BC = 12 cm, CA = 15 cm and AB = 18 cm, then the perimeter of the quadrilateral DEAF is :

1. 45 cm

2. 27 cm

3. 30 cm

4. 33 cm

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 BC and AC respectively.

⇒ DE || AB and DE = $\dfrac{1}{2} AB = \dfrac{1}{2}$ × 18 = 9 cm

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

⇒ FD || AC and FD = $\dfrac{1}{2} AC = \dfrac{1}{2}$ × 15 = 7.5 cm

AE = $\dfrac{1}{2}AC = \dfrac{1}{2} \times 15$ = 7.5 cm

AF = $\dfrac{1}{2}AB = \dfrac{1}{2} \times 18$ = 9 cm

Perimeter of AFED = AF + FD + DE + AE = 9 + 7.5 + 9 + 7.5 = 33 cm.

Hence, option 4 is the correct option.