If BC = 12 cm, AB = 14.8 cm, AC = 12.8 cm, the perimeter of quadrilateral BCYX is :

1. 31.8 cm

2. 15.9 cm

3. 29.8 cm

4. 32.8 cm

From figure,

X and Y are the mid-point of AB and AC respectively.

∴ BX = $\dfrac{AB}{2} = \dfrac{14.8}{2}$ = 7.4 cm and CY = $\dfrac{AC}{2} = \dfrac{12.8}{2}$ = 6.4 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.

In △ ABC,

∴ XY = $\dfrac{1}{2}BC = \dfrac{1}{2} \times 12$ = 6 cm.

Perimeter of BCYX = BC + CY + XY + BX = 12 + 6.4 + 6 + 7.4 = 31.8 cm

Hence, Option 1 is the correct option.